As they addressed reporters inside the Oval Office in mid-April, President Trump and his Salvadoran counterpart appeared to be operating in lock step.

The United States had just deported more than 200 migrants to a maximum-security prison in El Salvador, and President Nayib Bukele said his country was eager to take more. He scoffed at a question from a reporter about whether he would release one of the men who a federal judge said had been mistakenly deported.

“I mean, we’re not very fond of releasing terrorists into our country,” Mr. Bukele said.

But weeks earlier, when the three planes of deportees landed, it was the Salvadoran president who had quietly expressed concerns.

As part of the agreement with the Trump administration, Mr. Bukele had agreed to house only what he called “convicted criminals” in the prison. However, many of the Venezuelan men labeled gang members and terrorists by the U.S. government had not been tried in court.

Mr. Bukele wanted assurances from the United States that each of those locked up in the prison were members of Tren de Aragua, the transnational gang with roots in Venezuela, according to people familiar with the situation and documents obtained by The New York Times.

The matter was urgent, a senior U.S. official warned his colleagues shortly after the deportations, kicking off a scramble to get the Salvadorans whatever evidence they could.