WASHINGTON — President Obama said that he and other world leaders have offered Iran an “extraordinarily reasonable deal” that will test whether the leadership of the Islamic nation is serious about at last resolving the dispute over its nuclear program.

Even as negotiators appear close to an agreement, Mr. Obama highlighted the challenge of what comes next: ensuring that any pact forged in Geneva can pass muster in Tehran, where Ayatollah Ali Khamenei, Iran’s supreme leader, has expressed deep skepticism about a settlement with the outside world.

“We have made progress in narrowing the gaps, but those gaps still exist,” Mr. Obama said in an interview with CBS News that aired Sunday on “Face the Nation.” “And I would say that over the next month or so, we’re going to be able to determine whether or not their system is able to accept what would be an extraordinarily reasonable deal, if in fact, as they say, they are only interested in peaceful nuclear programs.”