More broadly, Mr. Obama and his top aides see the possibility of a new equilibrium between Sunni and Shiite groups in the region, a potential shift in alliances that worries America’s closest Arab allies, like Saudi Arabia.

In a press briefing at the White House on Thursday, Josh Earnest, the press secretary, said of the deal, “We’re hopeful that it might result in some kind of change emanating from Iran, but we’re certainly not counting on it.”

Despite White House hopes, many experts say it is naïve to expect that Iran, which provides critical military support to Mr. Assad as well as to the militant group Hezbollah in Lebanon, would be receptive to the administration’s overtures.

“I don’t see any evidence that Iran is increasingly disposed toward facilitating a negotiated solution to the Syrian crisis,” Frederic C. Hof, a former senior State Department official in the Obama administration and now an expert on Syria at the Atlantic Council, told reporters this week. “On the contrary, I think Iran and Hezbollah have been engaged in some very intensive consultations centering on the question of just how much of Assad’s Syria they will defend.”

Before his fight for the deal in Congress, Mr. Obama was far more open about his ultimate goals. In an interview in The Atlantic in March 2014, he said that a nuclear agreement with Iran was a good idea, even if the regime remained unchanged. But an agreement could do far more than that, he said:

“If, on the other hand, they are capable of changing; if, in fact, as a consequence of a deal on their nuclear program those voices and trends inside of Iran are strengthened, and their economy becomes more integrated into the international community, and there’s more travel and greater openness, even if that takes a decade or 15 years or 20 years, then that’s very much an outcome we should desire,” he said.

In a similar vein, Mr. Obama told The New Yorker, “If we were able to get Iran to operate in a responsible fashion — not funding terrorist organizations, not trying to stir up sectarian discontent in other countries, and not developing a nuclear weapon — you could see an equilibrium developing between Sunni, or predominantly Sunni, gulf states and Iran in which there’s competition, perhaps suspicion, but not an active or proxy warfare.”