A whirlwind weekend of prisoner exchanges, reduced sanctions and confirmation that Tehran has degraded its nuclear programme gives the US and Iran a "rare" chance to start a "new chapter", US and Iranian leaders said Sunday.

A vast array of Western sanctions targeting Iran were lifted on Saturday after the International Atomic Energy Agency confirmed that Iran had kept to its side of last year's landmark agreement with six major powers by significantly scaling down its nuclear programme.

Speaking separately on Sunday, US President Barack Obama and Iranian President Hassan Rowhani said they now see a path by which Iran could restore relations with the West.

"We have stretched our hands towards the world in a sign of friendship and begun a new chapter in our relations with the world after overcoming all the enmities, scepticism and schemes devised against us," Rowhani said in statement.

Obama expressed similar sentiments later in a White House address.

"You have a rare chance to follow a new path. You have to take advantage of that," he said, addressing the young people of Iran. "We can make this world safer for our children and our grandchildren for generations to come."

On top of the confirmation about Iran's nuclear systems and the lifting of sanctions targeting that programme, the weekend also saw the United States lift a decades-old freeze that blocked Iranian access to funds held at US institutions.

The freeze was implemented after the two countries broke off diplomatic ties in 1979 amid the Iranian Revolution, an event that saw militants storm the US embassy in Tehran and hold dozens of hostages for more than a year.

The deal, hammered out at a tribunal in the Hague, frees up 400 million dollars and another 1.3 billion dollars in interest, a figure that Obama referred to as a compromise that prevents Iran from seeking an even higher sum.

There is still more Iranian money locked up in US accounts. Obama said negotiations on the additional sums would continue.

Rowhani said earlier Sunday that Iran had regained access to more than 100 billion dollars in frozen assets.

Also Sunday, both sides confirmed the release Washington Post reporter Jason Rezaian, who had been detained by Iran for more than a year on espionage charges, and several other prisoners.

"We are relieved that this 545-day nightmare for Jason and his family is finally over," said Fred Ryan, the newspaper's publisher, in a statement.

Four US citizens were released from Iran and seven Iranians from the United States. Obama said none of the Iranians was being charged or investigated for terrorism. The US confirmed that its citizens had left Iranian territory.

The weekend's swap came on the heels of Iran's quick release of 10 US sailors who had been seized earlier in the week.

The US president praised the steps taken over the weekend to ease tensions, which had been achieved with diplomacy while ensuring that Iran's nuclear programme is hobbled.

"Whereas Iran was steadily expanding its nuclear programme, we have now cut off every path it could have used to build them up," he said.

Prior to his election in 2013, Rowhani, the moderate leader of the Islamic republic, promised to negotiate away the sanctions, which included an embargo on economically vital oil and gas exports.

Predicting an economic boom in the coming years, Rowhani promised Iranian youth that new opportunities will be created as Iran enters the "world economy orbit."

In his statement, Rowhani said that Iran was ready to relegate years of acrimony with the West to the past.

"We do not pose any threat to nations and governments. We are fully ready to protect Iran but we are also the messenger of peace, stability and security in the region and the world," he said.

While praising the deal for putting restraints on any Iranian nuclear ambition, Obama also seemed ready to accept the hand of friendship.

"We've achieved this historic result through diplomacy, without resorting to another war in the Middle East," he noted.

Obama added that the United States would remain vigilant of Iranian ambitions in the region, where the country backs rebel forces in Yemen and the regime in Syria against an array of opponents, some of whom had called for greater democracy there.

"We remain steadfast in opposing Iran's effort to destabilize elsewhere," said Obama, noting that some US sanctions will remain on Iran, particularly for its ballistic missile programme and the country's human rights violations.

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