Iran's media, including outlets close to the leadership, on Sunday hailed renewed talks with world powers as positive -- and claimed EU governments were now recognising Iran's atomic "rights".

The general message from hardline conservative dailies and state news agencies and television was that Iran had succeeded in defending its position in the talks in Istanbul on Saturday, and the next round of talks due in Baghdad next month could consolidate its gains.

State television IRIB and news agency IRNA both called the Istanbul round "interesting" with scope to build on points of agreement.

"EU Reaffirms Tehran's Nuclear Rights," the government-run English-language Iran Daily said on its front page under a photograph of EU foreign policy chief Catherine Ashton standing next to Iran's chief nuclear negotiator, Saeed Jalili.

The Fars news agency, seen as aligned with Iran's powerful Revolutionary Guards, said "the talks were based on respecting Iran's nuclear rights under the NPT," the nuclear Non-Proliferation Treaty that enshrines a state's right to peaceful atomic energy.

It quoted Jalili as saying: "We embark on providing for our needs on the basis of our rights and within the framework of the Non-Proliferation Treaty."

Press TV, a state-funded English-language broadcaster, quoted Jalili's deputy at the talks, Ali Baqeri, as saying: "The Islamic Republic of Iran's capabilities in various fields have created conditions which direct the other side towards respecting Iran's role."

The key to progress in the talks, the conservative newspaper Jomhuri Eslami said in an editorial, "is that America give up its political games and surrender to the realities" of Iran's nuclear progress.

That was an allusion to Iran's uranium enrichment programme, which has accelerated in recent months and is now increasingly producing fissile material enriched to 20 percent.

That level is required for a Tehran research reactor but is also a major step towards a weapons-grade 90 percent.

The Istanbul talks between Iran and the six powers -- Britain, China, France, Germany Russia and the United States -- were the first in 15 months.

They were aimed at generating the first steps towards building trust between the two sides and easing tensions that have built up over the West's suspicions that Tehran is seeking a nuclear weapons capability, despite its repeated denials.

It was notable in the talks that Iran showed a readiness to discuss its nuclear activities and the six powers made no mention of a total freeze of Iranian uranium enrichment -- the two issues that scuppered the last attempt at talks in 2011.

The next round in Baghdad is expected to get down to more substantive matters, particularly Iran's use of a bomb-proof bunker in Fordo to pursue uranium enrichment, and its refusal to allow UN inspectors to visit a military site thought to have carried out warhead design experiments.

The Javan newspaper, which reflects the views of hardliners, said that the mood in the Istanbul negotiations was "favourable" and appeared to show the West was shifting away from trying to bar Iran entirely from nuclear activities.

"They thought that by increasing pressure and sanctions they could prevail," it said. But "it is obvious that by seizing this opportunity and also accepting Iran's full right to nuclear activities, it will be more beneficial and less costly for the West."

Some papers highlighted the refusal of Iranian negotiators to hold a separate bilateral meeting with the US delegation to the Istanbul talks. "Iran's delegation said 'no' to the Americans," said the conservative Quds newspaper.