The Iranian president, Hassan Rouhani, ended a tumultuous week of diplomatic activity in New York with a striking offer to work rapidly to defuse tensions with America, hailing the US as "a great nation".

Speaking at a press conference at a hotel near United Nations headquarters, the newly-elected leader made the most conciliatory remarks heard from Tehran in a decade. He also offered to prepare a concrete plan for resolving the nuclear stalemate at a new round of negotiations in Geneva on 15 October.

He said Tehran might go even further, hinting at a possible confidence-building measure to be announced at the talks.

But it was Rouhani's tone that was most remarkable, at the end of a week in which he sought to present Iran as a reborn country, following his June election.

"The environment that has been created is quite different from the past, and those who have brought the change was the people of Iran," he said. "The first step has been taken here which is a beginning for better relations with other countries and in particular, between the two great nations of Iran and US. So the understanding between our peoples will grow and our governments will first stop the escalation of tensions, and then defuse those tensions."

The conciliatory language marks a radical change from the presidency of his predecessor, Mahmoud Ahmadinejad, and a break from tradition dating to the 1979 revolution of referring to the US as the "Great Satan". It mirrored a change on the streets of Tehran, where the ritual chanting of "Death to America" has almost died out at public gatherings since the elections.

Rouhani said that he was confident the decade-long impasse over Iran's nuclear programmes would soon be over, and he pointed to the friendly atmosphere at a meeting on Thursday evening between the Iranian foreign minister, Mohammad Javad Zarif, and his counterparts from the US, UK, France, Germany, Russia and China. The meeting was chaired by the European Union foreign policy chief, Catherine Ashton.

The Iranian president said the setting of a date for detailed negotiations in Geneva was "a positive step".

"In the talks in general there is a long of common ground," Rouhani said. "We have said that Iran will prepare a plan. Iran will prepare that plan and present it in Geneva and we hope that an even more positive step will be taken at Geneva to help settle the nuclear issue."

He did not go into specifics, but observers said it was a possible reference to the implementation of an early confidence-building measure. Rouhani indicated that the process of defusing tensions over the nuclear programme would be a phased but relatively swift affair, involving such trust-building steps.

"Step by step we will build confidence between our presidents and our countries. With sufficient will on both sides – and I assure you that on Iran's side the will is 100% – the nuclear file will be resolved in a short period of time," Rouhani said, rejecting suggestions that his flexibility at the negotiating table was constrained by hardline forces back in Iran. "My government has full authority in these negotiations with support from all three arms of government as well as the people of Iran. I have complete backing."

Western diplomats have said they were impressed by Zarif's businesslike approach at the foreign ministers' meeting on Thursday and said he put "new ideas" on the table that they did not describe.

"He made some suggestions about some ideas that they have. But I would say there's a lot more to understand," said a senior State Department official. "He laid out some thoughts that he had about what he thought this whole process might look like, what he thought might be some of the elements in a first step. And it was a very useful insight into Iranian interests, thinking, process, what their timeline is."