The government has reacted angrily to the union’s action, with far-right Finance Minister Bezalel Smotrich accusing it of playing into the hands of Hamas.
It is unclear how widely the stoppage will be observed, after several cities and municipalities announced they would not take part.
However, the call for a nationwide strike is the latest sign that public anger at the latest hostage killings is not about to subside.
The Israel Defense Forces (IDF) said earlier that the six bodies were found on Saturday in an underground tunnel in the Rafah area of southern Gaza.
The hostages were identified as Carmel Gat, Eden Yerushalmi, Hersh Goldberg-Polin, Alexander Lobanov, Almog Sarusi and Master Sgt Ori Danino.
The IDF said they had been killed shortly before its troops reached them on Saturday.
This triggered the demonstrations on Sunday, with crowds accusing the government and Mr Netanyahu personally of failing to save the remaining hostages.
Sunday’s protests were largely peaceful – but crowds broke through police lines, blocking a major highway in Tel Aviv.
Some people scaled buses and bins to gain a vantage point over the march, while others surrounded someone wearing a mask of Mr Netanyahu, chanting: “Alive, alive, we want them alive.”
One demonstrator held a sign which read: “You are the head. You are to blame”.
Protesters – many clad in Israeli flags – also descended on Jerusalem and other Israeli cities.
The demonstrations have overshadowed humanitarian efforts in Gaza, where the UN said on Sunday that the first full day of a campaign to vaccinate 640,000 children against polio had been successful.
The rollout relies on a series of localised pauses in fighting between Israeli forces and Hamas fighters, and the first three-day window began on Sunday.