John Kerry, US secretary of state, said diplomatic efforts to curb Iran’s nuclear programme had “earned the benefit of the doubt” after six major powers and Tehran gave themselves another seven months to strike a deal.

The P5+1, the five permanent members of the UN Security Council – the US, UK, France, Russia and China – and Germany, agreed to extend the so-called joint plan of action, under which the talks have taken place, until the end of June 2015 after failing to reach a deal after days of talks in Vienna.

Mr Kerry justified the extension saying the talks had “made real and substantial progress and we have seen new ideas surface”.

“Given how far we have come in the past year, and particularly in the past few days, this is not the time to get up and walk away.”

With political momentum building on Capitol Hill for new sanctions against Tehran, Mr Kerry appealed for patience from the US Senate.

“I have huge respect for the prerogatives of the US Congress,” he said, “But I believe this is a moment when congress [needs to] see the wisdom of leaving us the equilibrium for a few months.”

Philip Hammond, British foreign secretary, said the extension “does not mean that there will now be a lull in the negotiations.”

Iran’s centrist president, Hassan Rouhani whose political future depends on a nuclear deal, said on Monday he was certain that “this path of negotiations will lead to a final agreement, today or tomorrow”.

“The Iranian nation … will achieve a final victory. I have no doubt about it,” Mr Rouhani told state-run television. “The world has no choice but to talk to the representatives of the Iranian nation.”

The comments were a clear move by Iran’s president to help keep up the national spirit as many Iranians were disappointed to hear negotiations had been extended. “What if Iran nuclear talks continue for ever? This means sanctions will continue for ever.” said Banafsheh, a housewife.

Mr Rouhani said that “good progress” had been made in nuclear talks and “many gaps have been narrowed down” while only “some more steps still need to be taken”.

The president said that while Iran would not retreat from keeping nuclear technology, notably uranium enrichment, its diplomacy could lead to having “unfair” international sanctions, including the UN restrictions, lifted. “I promise centrifuges will not stop spinning, but people should also have good livelihoods,” he said.

Under the terms of the extension, Iran will continue to see about $700m of its assets unfrozen from international bank accounts every month, in return for an ongoing halt to all enrichment of uranium beyond the 5 per cent level.

The Vienna talks were due to end at midnight on Monday. But the French, German, UK foreign ministers and Mr Kerry concluded on Saturday night – over dinner at the British ambassador’s residence – that a deal was not going to happen without Tehran making an implausibly sharp turn in its negotiating position.

While a whole range of new technical proposals were discussed by diplomats over the weekend, the two sides remained deadlocked on the crucial issues of the number of centrifuges Iran wants to operate and the timing of a rollback of sanctions.

“We all believe that we have got far enough that it is worth continuing,” said Mr Hammond. But he added that it would be “invidious” to say progress had been made in any one area because “everything on the table is tentative”.

Many are sceptical that the P5+1 and Iran will be able to achieve a broad political consensus on a deal before March, given the way the last 12 months of discussions have already fared.

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“The objective would be to have an agreement that sets out in clear terms in layman’s language what we have agreed to do,” Mr Hammond said. “There will then be some further technical work while the tech experts translate that into very precise tech definitions of what will happen on the ground.”

The extension of talks poses a dilemma for both sides: on the one hand, negotiators need enough time to properly iron out the unresolved issues between the two sides; on the other hand, the longer the talks are extended, the easier a target they may prove for hardliners in Iran and conservative hawks in the newly Republican-controlled US Senate.

Both sides were deadlocked by fundamental disagreements that have dogged the talks since a preparatory summit in Oman at the beginning of the month.

Discussions shifted focus over the weekend from the core issue of uranium enrichment and the number of centrifuges Iran might be permitted to operate to issues including international observation and inspection.

As a result of the plan of action agreed with Tehran last November, the P5+1 gave themselves a year to wind back Iran’s ability to build a nuclear weapon in return for an end to international economic sanctions.

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