President Bukele praised the late police chief as “a fundamental part of bringing peace and security to our people”.
Mr Bukele said he would request international help to examine the causes of the crash.
El Salvador’s Armed Forces said the UH-1H helicopter came down near Pasaquina, some 10km (six miles) from the border with Honduras.
The helicopter was carrying Police Chief Arriaza, Mr Coto and a TV news crew, according to local media.
All those on board died in the crash, the Salvadorean military said.
Mr Arriaza had travelled to the Honduran border to take Mr Coto into custody.
Honduran officials said police had captured the former bank director as he was trying to make his way to the US with the help of a people-smuggler.
News of his arrest caused surprise and confusion as it was not widely known that he had been on the run.
In fact, the Salvadorean authorities had announced back in July that Mr Coto had been detained in Panama.
It is not clear how he came to be in Honduras.
Mr Coto was one of 32 people accused of embezzlement and money-laundering over the disappearance of $35m from the coffers of the COSAVI credit union.
El Salvador’s attorney-general accused the group of syphoning off money from people’s savings and using it to buy luxury flats and cars, among other items.
In total, 15 people have been detained in connection with the case. Among them are Mr Coto’s parents.