WASHINGTON — Lawmakers from both parties, deeply mistrustful of a leader who has brutalized his own country, greeted a joint agreement between the United States and North Korea coolly on Tuesday, with top Republicans warning President Trump that any final accord on Kim Jong-un’s nuclear program should be submitted to the Senate for ratification.

The president’s allies on Capitol Hill said the talks represented a potential breakthrough that could lead to lasting peace with one of the United States’ most dangerous enemies. But even they agreed with more skeptical lawmakers that there was much work to be done.

Others, including leading Republican foreign policymakers, said it was unclear what, if anything, had been gained by the United States in exchange for the benefits accrued to Mr. Kim.

“While I am glad the president and Kim Jong-un were able to meet, it is difficult to determine what of concrete nature has occurred,” Senator Bob Corker of Tennessee, the chairman of the Senate Foreign Relations Committee, said in a notably brief statement.