In the fall of 2016, the Obama administration sealed a major military agreement with Israel that committed the United States to giving the country $38 billion in arms over 10 years.

“The continued supply of the world’s most advanced weapons technology will ensure that Israel has the ability to defend itself from all manner of threats,” President Barack Obama said.

At the time, the agreement was uncontroversial. It was a period of relative calm for Israel, and few officials in Washington expressed concern about how the American arms might one day be used.

Now that military aid package, which guarantees Israel $3.3 billion per year to buy weapons, along with another $500 million annually for missile defense, has become a flashpoint for the Biden administration. A vocal minority of lawmakers in Congress backed by liberal activists are demanding that President Biden restrict or even halt arms shipments to Israel because of its military campaign in Gaza.

Mr. Biden has been sharply critical of what he on one occasion called “indiscriminate bombing” in Israel’s war campaign, but he has resisted placing limits on U.S. military aid.

The United States and Israel have had tight military relations for decades, stretching across multiple Democratic and Republican administrations. Israel has purchased much of its critical equipment from the United States, including fighter jets, helicopters, air defense missiles, and both unguided and guided bombs, which have been dropped in Gaza. Legislation mandates that the U.S. government help Israel maintain force superiority — or its “qualitative military edge” — over other Middle Eastern nations.

The process of arms delivery to Israel is opaque, and the pipeline for weapons to the country is long. The United States has sent tens of thousands of weapons to the country since the Oct. 7 killings by Hamas attackers, but many were approved by Congress and the State Department long ago and funded with money mandated by the Obama-era agreement, known as a memorandum of understanding.

“At any given time, delivery on these sales is constantly taking place,” said Dana Stroul, who recently departed as the Pentagon’s top official for Middle East affairs.

Mr. Biden has the power to limit any foreign arms deliveries, even ones previously approved by Congress. Far from cutting off Israel, however, he is pushing a request he made shortly after the Oct. 7 attacks for $14 billion in additional arms aid to the country and U.S. military operations in the Middle East. The money has been stalled in Congress amid disputes over Ukraine aid and U.S. border security and faces growing Democratic concern.

Because of a legal loophole, the State Department does not have to tell Congress and the public about some new arms orders placed by Israel since Oct. 7 since they fall below a certain dollar value. Congressional officials have criticized the secrecy, which stands in contrast to the Biden administration’s public fanfare around arms deliveries to Ukraine.

Since the Hamas attacks, State Department officials have continued to authorize arms shipments to Israel that are tranches of orders, or what officials call “cases,” approved earlier by the department and by Congress — often years ago, and often for delivery in batches over a long period. Officials describe this step as pro forma. The authorizations have occurred almost daily in recent weeks, and are in line with Mr. Biden’s policy of giving full support to Israel.

But Mr. Biden hinted on Thursday about a possible shift. In a phone call with Prime Minister Benjamin Netanyahu of Israel, Mr. Biden warned that U.S. policy could change if Israel did not take more action to protect civilians and aid workers in Gaza, according to a White House summary of the conversation.

Israel regularly receives arms from the U.S. Defense Department, as well as directly from American weapons makers. The largest arms orders are often filled over years in smaller groups of specific items. For such cases, arms buyers like Israel come to the U.S. government saying they are ready to pay for part of an order.

When the Defense Department is supplying the arms — which includes the most expensive weapons systems — the State Department then tells the Pentagon to issue a letter of acceptance to the buyer. That authorization is often a pro forma step, and a buyer signing it means there is now a legal contract to fill that part of the larger order.

The State Department’s Bureau of Political-Military Affairs, which manages foreign defense relationships and arms transfers, typically acts within two days of hearing about a buyer’s fulfillment request to tell the Defense Department to issue the letter. If defense officials decide to fill the case by placing an order with a U.S. weapons maker, the assembly and shipment would normally take years.

For Israel’s immediate needs since Oct. 7, defense officials have drawn from U.S. military stockpiles, including one in Israel.

Israel and other nations also sign contracts directly with American weapons makers. These orders go through a State Department review (and occasionally congressional review, depending on the price tag). The State Department regularly issues four-year export licenses to the companies, and provides less public information on commercial orders.

Israel is awaiting State Department approval for 24,000 assault rifles it requested before Oct. 7 — a direct commercial order that has drawn scrutiny from some officials in the department and lawmakers because of Israeli settler violence against Palestinians in the West Bank.

Since Oct. 7, Israel has asked the United States to expedite filling cases from long-existing orders, U.S. officials said. State and Pentagon officials have complied.

Given the politics around Israel, any change would have to come from Mr. Biden.

Israel’s recent requested fulfillments — and the resulting drawdowns from U.S. stockpiles — have included munitions ranging from 250- to 2,000-pound bombs. Many cases have been for 500-pound bombs, said a U.S. official, who like others spoke on the condition of anonymity because of the sensitivities and opacity around arms sales.

Some of what Israel has requested since Oct. 7 is meant to enhance its defenses against actors besides Hamas, including Hezbollah and other Iran-backed militias in the region, as well as Iran itself. U.S. officials say one reason for their reluctance to limit arms sales to Israel is the risk of weakening its deterrence against those foes.

Shortly before seven aid workers for World Food Kitchen were killed in Israeli airstrikes on Monday, State Department officials told the Pentagon to issue a letter of acceptance to Israel for a case of munitions, U.S. officials said.

That batch follows other shipments sent to Israel over the years to fulfill large munitions orders approved by Congress and the State Department in both 2012 and 2015, U.S. officials said.

In rare instances, an assistant secretary of state has asked department officials to refrain from telling Pentagon counterparts to issue a letter of acceptance because of concerns about the customer country, said Josh Paul, who resigned from the department’s political-military bureau in October to protest Mr. Biden’s war policy.

“They can say, ‘You know what, we changed our minds,’” Mr. Paul said, stressing that top U.S. officials can intervene at any point before the customer receives a title of ownership. Even then, there have been instances — notably with Turkey and Pakistan — in which senior American officials have stopped a transfer after the countries received the titles.

Since Oct. 7, Israel has placed new orders. The State Department only needs to notify Congress when a price tag is above a certain threshold. That amount varies by country and the type of military aid. If Israel orders a major weapons system, the department only tells Congress if the tranche is valued at more than $25 million.

Congressional officials are pushing the State Department to give them more information on orders that fall below the price tag threshold.

At least three of the new Israeli orders have crossed the threshold required for congressional review, however — and Secretary of State Antony J. Blinken bypassed that twice. Last December, Mr. Blinken invoked a rare emergency authority to avoid legislative review and push through two of those orders worth $253 million in total, for tank ammunition and for artillery shells. The Pentagon then drew from U.S. stockpiles to send those quickly to Israel.

The State Department told Congress in January about a third one — an $18 billion order of F-15 jets that Israel placed after Oct. 7. The department is seeking approval from four lawmakers on two congressional committees with oversight of arms transfers. Two Republicans approved the order in January, a U.S. official said, and two Democrats apparently have not so far.

The Biden administration is pressuring the Democratic lawmakers to approve the order, after which the State Department would officially notify it. The order is one of the biggest from Israel in years. The first jets would not be delivered until 2029 at the earliest, one official said.

And Israeli officials are expected to place an order for F-35 jets soon, U.S. officials said. If the administration tried to ram an order past informal congressional review, lawmakers could seek to block that through a supermajority joint resolution during the notice period. But even if such a resolution passed in both chambers, the president could veto it.

Martin Indyk, a special envoy for Israeli-Palestinian negotiations in the Obama administration, said “the problem with this American largess is that it has bred a sense of entitlement among Israelis over the years.”

Israel’s dependence on the United States has grown “exponentially because its deterrent capability collapsed on Oct. 7,” he said, noting that Israel would need the U.S. military to help ward off major assaults by Hezbollah or Iran. The Biden administration needs to use that leverage to shape the Israeli government’s behavior, he added.

Within the State Department, there has been some dissent about the arms transfers, reflected in three cables sent to Mr. Blinken last fall and in an internal exchange after a recent White House move.

Mr. Biden issued a national security memorandum in February requiring all recipients of U.S. military aid to provide written promises that their forces abide by international law. The move was intended to defuse growing pressure in Congress.

Critics say the exercise adds little to existing U.S. requirements that military aid recipients observe international and humanitarian law.

After Israel submitted its assurances last month, officials in the two State Department bureaus that focus on human rights and on refugees raised concerns with Mr. Blinken about Israel’s commitment, a U.S. official said. But Mr. Blinken accepted Israel’s assurances.

Speaking in general terms, Matthew Miller, the State Department spokesman, said last month that when it comes to Israel, U.S. officials “have had ongoing assessments about their compliance with international humanitarian law.”