Iran's new president, Hassan Rouhani, declared that "peace is within reach" on Tuesday, in a hotly anticipated speech at the United Nations in which he offered immediate negotiations aimed at removing any "reasonable concerns" over his country's nuclear programme.

Rouhani argued that in return, Iran wanted the international community to recognise its right to enrich uranium, the issue that has been at the heart of the diplomatic impasse over the past 11 years.

The Iranian president, elected in June, was speaking a few hours Barack Obama had stood at the same podium and pledged to focus his administration's foreign policy in its remaining three years on the Middle East, particularly on reaching a diplomatic settlement in Iran.

Obama assigned his secretary of state, John Kerry, to oversee negotiations with Tehran and offered Rouhani an important symbolic gesture, making the first official US acknowledgement of the CIA's well-documented role in the ousting of Iran's democratically-elected government in 1953.

But despite the positive gestures a much-anticipated meeting between the two leaders not materialise. The White House said it offered to arrange a discussion in the margins of the general assembly but said that Rouhani's office deemed it was "too complicated".

He did not go into details and a meeting with Barack Obama did not materialise. The White House said it offered to arrange a discussion in the margins of the general assembly but said that Rouhani's office deemed it was "too complicated".

In his speech however, Rouhani said he had "listened carefully" to Obama address earlier in the day. He concluded that if Washington did not give in to the influence of "warmongers", then the US and Iran "can arrive at a framework to manage our differences".

The framework Rouhani suggested for dealing with the stand-off over Iran's nuclear aspirations offered a trade between increased Iranian transparency and international recognition of Iran's right to enrich.

"Our national interests make it imperative that we remove any and all reasonable concerns about Iran's peaceful nuclear programme," he said, adding that Iran "is prepared to engage immediately in time-bound and result-oriented talks to build mutual confidence and the removal of mutual uncertainties with full transparency."

On the other hand, he said that the country's mastery of the technology had reached such an "industrial scale", and so could not longer be reversed. So the world should instead recognise Iran's basic right to carry out all parts of the nuclear fuel cycle.

The vague nature of Rouhani's offer, the accusatory tone of much of the rest of his speech, and the failure to organise a meeting with Obama all served to dampen expectations of an immediate breakthrough.

Diplomats and observers at the UN said it was clear that Rouhani's speech was principally aimed at a domestic audience, particularly Iran's supreme leader, Ali Khamenei and the regime's hardliners who are suspicious of Rouhani's charm offensive in the West.

In his UN speech earlier in the day, Obama made clear that the US saw the Iranian nuclear programme as a more immediate and serious threat to its core interest. He responded to the overtures of the newly-elected leadership in Tehran by putting Kerry in charge of the coming critical weeks of intense negotiations.

"Given President Rouhani's stated commitment to reach an agreement, I am directing John Kerry to pursue this effort with the Iranian government, in close coordination with the European Union, the United Kingdom, France, Germany, Russia and China," the president said. A senior administration official described the move as "a significant elevation" in the status of the talks.

It move mirrored Rouhani's decision to put his own foreign minister, Mohammad Javad Zarif, in charge of the talks from the Iranian side, breaking from the practice of the past eight years of abortive negotiations of assigning them to senior officials. The foreign ministers of all seven countries are due to meet for the first time at the UN on Thursday.

"Directing secretary Kerry to lead this, signals that the negotiations may be elevated to the foreign minister level, which would be very good news," said Trita Parsi, the head of the National Iranian American Council, and the author of a book on US-Iranian negotiations, A Single Roll of the Dice.

"This means that far greater political will is being invested into the diplomatic process, which in turn increases the cost of failure. That is exactly what is needed to overcome the political obstacles to a deal." Obama acknowledged the difficulties ahead. "The roadblocks may prove to be too great, but I firmly believe a diplomatic path must be tested," he said.

Obama offered Rouhani an important symbolic gesture, making the first official US acknowledgement of the CIA's well-documented role in the ousting of Iran's democratically elected government in 1953. "This mistrust has deep roots. Iranians have long complained of a history of US interference in their affairs, and America's role in overthrowing an Iranian government during the cold war," he said.

The reference to the CIA's part in the ousting of Mohammad Mosaddegh, Iran's democratically elected leader, marked a first official admission of that role, and represented an important gesture to Rouhani. It will be seen in Iran as a diplomatic victory and belated acknowledgement of a long-festering Iranian sense of injustice. The coup, supported by both the US and the UK, paved the way for the dictatorship of the shah, and then the 1979 Islamic revolution against it.

"I don't believe this difficult history can be overcome overnight. The suspicions run too deep. But I do believe if we can resolve the issue of Iran's nuclear programme that can be a major step," Obama said.

The US president expressed optimism about this week's talks. "We should be able to achieve a resolution that respects the rights of the Iranian people, while giving the world confidence that the Iranian programme is peaceful. To succeed, conciliatory words will have to be matched by actions that are transparent and verifiable."

Thursday's talks involve Rouhani's foreign minister, Mohammad Javad Zarif, Kerry, the UK foreign secretary, William Hague and foreign ministers from Russia, China, France and Germany.

Much will depend on how far Rouhani is prepared to go to remove what he described as the "reasonable concerns" about Iran's nuclear intentions. If that involves Iran's acceptance of strict limits on the degree of enrichment allowed and a stricter regime of inspections, there may room for a deal.