Mr. Obama is facing a double bind over the next two months with the deal pending. Iran’s supreme leader, Ayatollah Ali Khamenei, has suggested that his country will not comply with crucial conditions, including unfettered access to nuclear sites. He has insisted that sanctions be lifted immediately after a deal is signed, something the United States has said would not happen. Closer to home, the Republican-led Congress is demanding review power over any agreement, and will begin considering bipartisan legislation next week that would allow them to review the deal, vote to disapprove it and limit Mr. Obama’s ability to waive sanctions.

Some Republican critics of the accord, including Mr. McCain, have seized upon the assertions of Iran’s leaders to argue that Mr. Obama is on the brink of ceding too much in the talks.

“It’s not surprising to me that the supreme leader or a whole bunch of other people are going to try to characterize the deal in a way that protects their political position, but I know what was discussed in arriving at the political agreement,” Mr. Obama said.

As for Congress, he said he had talked to Senator Bob Corker, Republican of Tennessee, the chairman of the Foreign Relations Committee and a sponsor of the review bill, and Senator Benjamin L. Cardin of Maryland, the panel’s senior Democrat, about how to give Congress a voice in the debate.

“I want to work with them so that Congress can look at this deal when it’s done,” Mr. Obama said. “What I’m concerned about is making sure that we don’t prejudge it,” he added, or allow opponents of the deal to “try to use a procedural argument essentially to screw up the possibility of a deal.”