UNITED NATIONS – Barack Obama and Hassan Rouhani spoke Friday by telephone in the first conversation between the presidents of the United States and Iran in more than 30 years, a stunning and unexpected development that may boost prospects for settling the years-long standoff over Iran’s nuclear program and other longstanding divisive issues.

Obama made the unplanned call to Rouhani as the Shiite Muslim cleric was being driven to John F. Kennedy International Airport after a four-day visit to New York that marked his debut on the world stage following his June election.

Both men announced the conversation shortly after it took place, Rouhani on his Twitter feed and Obama at a White House appearance that had been scheduled to discuss a budget impasse with Congress.

Iran’s mission to the United Nations released a four-line statement, saying the two discussed “different issues,” including the need “for expediting a resolution of the West’s standoff with Iran over the latter’s nuclear program.”

Experts on Iran used a wide range of superlatives to discuss the call.

Suzanne Maloney, a senior fellow at the Brookings Institution’s Saban Center for Middle East Policy and the editor of its [email protected] blog, called it “hugely positive,” while Sam Brannen, a senior fellow at the Center for Strategic and International Studies, another Washington think tank, said it was a “historic but long overdue moment.” National Security Adviser Susan Rice, speaking on CNN, called it a “ground-breakng event.”

It was just one of what had been a week of unprecedented developments in the tense U.S.-Iran relationship, including a surprise one-on-one meeting Thursday between U.S. Secretary of State John Kerry and Iranian Foreign Minister Javad Zarif.

Only a few hours before the phone conversation, Rouhani had used a news conference in New York to chip away at another tension in the relationship, expressing hope that his trip would be a “first step” toward ending Iran’s international isolation and decades of animosity between “the two great nations of Iran and the United States of America” — remarkable phrasing for a member of a ruling theocracy that has for three decades denounced America as “The Great Satan.”

Maloney, the Brookings fellow, said Iran watchers were stunned by the phone call. “It is of an order of magnitude beyond anything that I think anyone would’ve imagined,” she said.

The phone call lasted only 15 minutes, but it offered the best hope in years for the two countries to settle their disagreements over Iran’s nuclear program and showed that both men believe conditions are right to risk a complex undertaking with no assurance of success.

Both men are likely to encounter fierce resistance from domestic opponents and close allies, especially Israel in the case of the United States.

In describing how the call came about, a senior U.S. official in Washington said that Iranian officials contacted American counterparts and told them that Rouhani wanted to speak to Obama.

The president returned the call about 2:30 p.m., according to the senior U.S. official, who could not be identified under the conditions of the briefing.

During the call, Obama expressed concern about three Americans, including former FBI agent Robert Levinson, a South Florida resident who disappeared from the Iranian island of Kish in 2007.

The other two are Amir Hekmati, a former Marine of Iranian descent who is being held on espionage charges, and Saeed Abedini, an Iranian-American Christian who has been sentenced to eight years in prison for evangelizing.

After the call, the administration notified congressional leaders and Israel — the latter an indication of the sensitivity with which any U.S. rapprochement with Iran would be viewed in that country.

Israeli Prime Minister Benjamin Netanyahu, who has long portrayed Iran’s nuclear threat as an existential threat to Israel, is scheduled to meet with Obama on Monday.