WASHINGTON – For the past six years, the Iranian president's speech at the annual gathering of the United Nations has been met by a ritual walkout of Western diplomats. This year, they're likely to hang around till the end — and some may even applaud.

Instead of the angry diatribes of former President Mahmoud Ahmadinejad, Hassan Rowhani, his soft-spoken successor, is likely to give a conciliatory address to world leaders this week. It will be closely watched for signs that he is willing to thaw relations with the West.

Western diplomats predict that Rowhani's speech Tuesday at the U.N. General Assembly will include an important gesture, perhaps an acknowledgment of the Holocaust. U.S. officials would like to see him go further during his five-day visit, possibly by consenting to direct talks with Washington for the first time since diplomatic relations were ruptured by the 1979 Islamic Revolution.

The White House says it has not scheduled a meeting between President Obama and the 64-year-old cleric. But U.S. officials have dropped hints that Obama and other top officials are ready for impromptu chats with Rowhani or his U.S.-educated foreign minister, Mohammad Javad Zarif, that could open the way for bargaining on Iran's disputed nuclear program.

Obama has repeatedly signaled his willingness for direct contact, both in remarks and in a recent exchange of letters with Rowhani, who was elected in June after a campaign that included pledges to ease Iran's isolation and improve relations with the West.

Iran's most powerful figure, supreme leader Ayatollah Ali Khamenei, has long resisted compromise on the nuclear program. But with punitive sanctions increasingly squeezing the economy, he has signaled top-level support for the Rowhani mission, including allowing the release of 11 political prisoners. Most had been held since the government crackdown that followed Ahmadinejad's disputed re-election in 2009.

"After eight years of an erratic, unpredictable president who would say outlandish things, you have a normal person as the president of Iran," said Haleh Esfandiari, a former political prisoner under Ahmadinejad who now heads the Middle East program at the nonpartisan Woodrow Wilson International Center for Scholars in Washington. "He is centrist, he is a moderate, he tries to compromise — a word that did not exist in President Ahmadinejad's lexicon."

The question is whether Rowhani and his aides realize they'll have to accept stiff limits on their nuclear program before Washington and its allies unravel the web of sanctions that have cut Iranian oil exports in half, battered the currency and created rampant inflation.

Analysts say Obama must be careful not to look too eager to make a deal. That would undermine his negotiating leverage and alienate influential Iran hawks in Congress, as well as the Israelis, who are counting on the United States to prevent Tehran from getting a nuclear bomb.