WASHINGTON — The meeting in the Oval Office in late June was called to give President Obama and the four top members of Congress a chance to discuss the unraveling situation in Iraq.

But Harry Reid, the Senate majority leader, wanted to press another point.

With Mitch McConnell, the Republican leader, sitting a few feet away, Mr. Reid complained that Senate Republicans were spitefully blocking the confirmation of dozens of Mr. Obama’s nominees to serve as ambassadors. He expected that the president would back him up and urge Mr. McConnell to relent.

Mr. Obama quickly dismissed the matter.

“You and Mitch work it out,” Mr. Obama said coolly, cutting off any discussion.

Mr. Reid seethed quietly for the rest of the meeting, according to four separate accounts provided by people who spoke with him about it. After his return to the Capitol that afternoon, Mr. Reid told other senators and his staff members that he was astonished by how disengaged the president seemed. After all, these were Mr. Obama’s own ambassadors who were being blocked by Mr. McConnell, and Secretary of State John Kerry had been arguing for months that getting them installed was an urgent necessity for the administration.