TEHRAN, Iran — Iranians from across the political spectrum hailed Saturday the historic phone conversation between President Barack Obama and his Iranian counterpart Hassan Rouhani, reflecting wide support for an initiative that has the backing of both reformists and the country’s conservative clerical leadership.

Despite the broad-based praise, the hard-liners opposed to any improved contact with Washington made their objections clear at Rouhani’s arrival in Tehran. Several dozen protesters chanted “Death to America” and tried to block Rouhani’s motorcade. The semiofficial Mehr news agency reported that at least one demonstrator hurled a shoe — a common gesture of contempt in the Middle East — in the direction of Rouhani. Other reports said eggs were thrown at his car.

“Dialogue with Satan is not ‘hope and prudence,'” some chanted, using the Rouhani’s campaign from the June election.

Rouhani supporters, meanwhile, greeted his return from New York with cheers placards thanking him for seeking peace instead of confrontation. One banner read: “Yes to peace, no to war.”

Rouhani now has the difficult mission of trying to unite the country behind his outreach to ease a three-decade-long estrangement with the U.S. and move toward a possible settlement to roll back sanctions imposed over Tehran’s nuclear program. Rouhani’s effort appears to have the critical backing of Supreme Leader Ayatollah Ali Khamenei.

But even the endorsement from Iran’s most powerful figure is not enough to silence criticism of the fast-paced developments during the past days.

Alaeddin Boroujerdi, who heads Parliament’s foreign policy and national security committee, was quoted by Iranian media as saying that the 15-minute telephone talk with Obama on Friday showed Iran’s “might.” But the hardline rajanews.com news website said there was no justification for Rouhani to talk to the “Great Satan,” its term for the United States, and that the conversation was “a strange and useless step.”

Rouhani has followed a policy of moderation and easing tensions with the outside world, a marked distance from the bombastic style of former president Mahmoud Ahmadinejad. Rouhani says Iran is ready to provide assurances that Iran’s nuclear program won’t be weaponized by offering greater transparency and cooperation. He has demanded lifting of sanctions in return.

The West says Iran’s program aims at developing weapons technology, while Tehran says it is for peaceful purposes.

Iran’s stock exchange reacted positively to the historic phone conversation between the two leaders, with the index improving by 687 points, to 46,400 on Saturday. The rial, Iran’s national currency, strengthened against the U.S. dollar as the news broke. The dollar was trading at 29,500 rials in foreign currency shops, compared to 30,200 rials on Thursday.

“Historic contact on the flight back home” was the front-page headline in the moderate Etemad daily Saturday. Arman, another newspaper, wrote: “The world was caught by surprise.”

Upon returning home, Rouhani told reporters that the U.S. gave him a 2,700 year-old artifact, interpreted as a new token of friendship between the United States and Iran. The artifact had been in New York since 2003, when an art dealer smuggled it into the U.S. from Iran.

Mina Yazdi, a Tehran resident, said she was “very happy” to hear about Rouhani’s phone conservation with Obama, which was organized after Rouhani’s staff reached out to the White House with the proposal. The two leaders were both at the U.N. on Tuesday following speeches to the General Assembly, but did not meet.

“I hope that, after these talks, the economic problems of Iranians are eased,” said Yazdi.

Prominent conservative figures — including Friday prayer leaders, who are all loyal to Khamenei — have publicly endorsed Rouhani’s “heroic flexibility,” citing the phrase Khamenei used last week to encourage diplomatic outreach but remain aware of the nation’s strategic interests.

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