TEHRAN  - Iran's leaders lauded the interim nuclear deal struck with world powers on Sunday as recognition of its "right" to enrich uranium and the start of an end to punishing sanctions.

Backed by top decision-maker Ayatollah Ali Khamenei, President Hassan Rouhani said the agreement with world powers at talks in Geneva signalled acceptance of the principle of uranium enrichment in Iran.

Rouhani also said the breakthrough deal showed that punitive sanctions slapped on Iran over its controversial nuclear programme were starting to crumble.

"Iran's right to uranium enrichment on its soil was accepted in this nuclear deal by world powers," he said in a speech broadcast live on state television.

"The sanctions regime will begin to shatter with the (implementation) of this agreement," Rouhani said, adding that the talks in Geneva had sparked "cracks" in the structure of sanctions.

Iran's supreme leader Khamenei paid tribute to the "achievement" of the Iranian negotiating team in clinching the long-elusive nuclear deal with world powers.

"The nuclear negotiating team should be thanked and appreciated for this achievement. God's grace and the support of the Iranian nation were the reasons behind this success," he said, quoted by Fars news agency. "Resistance against excessive demands should be the criteria for (nuclear) officials," added Khamenei, who had stressed during the negotiations that Iran's "right" to enrich uranium was a red line.

In a letter to Khamenei, Rouhani said the agreement was in the interests of the region and world peace. "This agreement benefits all regional countries and global peace," Fars quoted him as saying. "Iran's nuclear and enrichment rights were recognised by world powers."

And on Twitter, the Iranian president forecast that the deal would "open new horizons". The deal had been made possible due to "Iranian people's vote for moderation," he said, referring to his surprise election victory in June against a pool of conservatives. The historic deal came after intensive negotiations since Wednesday between Iranian interlocutors and high-ranking delegations from the United States, Britain, France, China and Russia plus Germany in the grouping known as the P5+1. The talks had hit snags over a few points of difference, including Iran's insistence to have what it calls its "right" to enrich uranium to be recognised by the six major powers.

The White House said such a right was not inserted in the deal, although a senior Iranian negotiator, Abbas Araqchi, said Iran's "enrichment programme" had been recognised.

Foreign Minister Mohammad Javad Zarif, speaking to Iranian journalists, said the recognition was implicit as it was included in Article Four of the nuclear Non-Proliferation Treaty, of which Iran is a signatory.

Under the deal which followed a decade of failed diplomacy and rising tensions, Iran agreed to curb its nuclear programme in exchange for sanctions relief.

Tehran is to limit uranium enrichment - the area that raises most suspicions over Iran's alleged nuclear weapons drive - to low levels.

It will neutralise its entire stockpile of uranium enriched to medium 20-percent purities - close to weapons-grade - within six months, US Secretary of State John Kerry said.

Iran will also not add to its stockpile of low-enriched uranium, nor install more centrifuges or commission its Arak reactor.

UN atomic inspectors will also have additional, "unprecedented" access, Kerry said in Geneva.

In exchange, Iran is to receive some $7 billion in sanctions relief and world powers vowed not to impose new embargo measures for six months if it sticks by the accord.