John Kerry arrived in Geneva on Saturday morning to join William Hague and other foreign ministers in negotiations on Iran's nuclear programme.

The Russian foreign minister, Sergey Lavrov arrived on Friday afternoon for talks with his Iranian counterpart, Mohammed Javad Zarif.

France's Laurent Fabius also arrived on Saturday morning, where Germany's Guido Westerwelle and China's Wang Yi were expected to join him in what is hoped will be a final push towards a deal that has eluded diplomats for over a decade.

They are also expected to use the weekend for preparations for a Syrian peace conference in Geneva next week.

The presence of so many foreign ministers did not guarantee a nuclear agreement with Iran was ready to be signed, diplomats at the talks cautioned.

The same ministers took part in the Geneva talks two weeks ago but fell short of a deal despite three days of intense and complex negotiations.

But a senior European diplomat told reporters that the foreign ministers would come to Geneva only if there was a deal to sign, Reuters reported.

"We have made progress, including core issues," the diplomat said.

Fabius, who spoke out against a draft deal floated at the 7-9 November negotiating round, appeared guarded on arrival in Geneva, Reuters reported.

"I hope we can reach a deal, but a solid deal. I am here to work on that," he said.

A French diplomatic source urged caution, saying: "It's the home stretch, but previous negotiations have taught us to be prudent."

Announcing Kerry's departure from Washington late on Friday night, after the secretary of state had been to visit the grave of John F Kennedy, the state department said he would fly to Switzerland – not necessarily to clinch a deal – but "with the goal of continuing to help narrow the differences and move closer to an agreement".

A US official said: "Kerry's not going to wait to see if there is an agreement and then take 10 hours to get here. He wants to get here and help push it along."

However, there was growing hope in Geneva on Friday night that the last remaining obstacles to a deal were in the process of being ironed out.

In Paris before his departure, Fabius said: "You know our position ... it's a position based on firmness, but at the same time a position of hope that we can reach a deal."

China's state-run Xinhua news agency quoted foreign ministry spokesman Hong Lei as saying the talks had "reached the final moment", Reuters reported.

The EU foreign policy chief, Catherine Ashton, who chairs the talks, held discussions with the Iranian delegation late into the night.

If a deal is reached, it would fend off the threat of a new war in the Middle East and buy six months for diplomacy aimed at a long-term settlement to the long-running and perilous international standoff over Iran's nuclear aspirations.

To that end, the draft deal on the table on Saturday will exchange curbs on Iran's nuclear activity for limited sanctions relief for the six-month period.

Iran would get access to some frozen bank accounts and could start trading again in gold, petrochemicals, vehicle and aircraft parts. In exchange, Iran would stop or reverse different parts of its nuclear programme.

Agreeing on exact terms has so far taken three rounds of talks in Geneva since a reformist president, Hassan Rouhani was elected in Iran.

Officials have consistently said there was a strong will to find common ground on all sides but that decades of distrust and the extreme complexity of the nuclear issue had hampered progress.

There were unconfirmed reports on Friday night that one of the most intractable of the outstanding issues, the question of Iran's right in principle to enrich uranium, had been resolved with the drafting of a form of words in the draft agreement that satisfied both sides.

Sources said the most important remaining obstacle was the extent to which work should be allowed to continue at a heavy water reactor in Arak, which would produce plutonium when completed.

"Yesterday we talked about the issues we don't agree on and naturally delegations needed to consult their capitals. In some cases, we have had results," the Iranian foreign minister, Mohammad Javad Zarif, who leads the country's delegation, said.

"In some cases a number of phrases have been added [to the text] and we still need to do some work in other cases. We are dealing with an issue that was the subject of difference for 10 years."

Reza Marashi, a former US state department official now at the National Iranian American Council, said: "If Iran does not get wording on the right to enrich, then the deal is unbalanced in the west's favour. They get verifiable limits and roll-back on every single critical element of the Iranian programme, and Iran would just get access to its own money."

According to sources at the talks, a compromise deal on the Arak heavy water reactor had been written into the text of the draft agreement at the last Geneva round which ended on 10 November.

Under that compromise, Iran would cease work on making fuel rods but would continue other elements at the long-delayed project.

However, on French insistence, the paragraphs on Arak were put back into brackets, meaning they were open to negotiation again. In response, Iran asked for concessions elsewhere to "rebalance the deal".

Earlier on Friday, Britain's ambassador in Washington urged the US Congress not to impose new sanctions on Iran while delicate nuclear negotiations are making progress in Geneva.

Peter Westmacott made his appeal as the latest round of talks entered its third day.

"The deal currently under negotiation would be a meaningful first step, immediately improving our national security and that of our partners in the region. This is, therefore, a critical week for diplomacy," Peter Westmacott wrote in the Washington political website The Hill.

"Many gaps between the parties have been bridged altogether; those that remain have narrowed considerably.

"But further sanctions now would only hurt negotiations and risk eroding international support for the sanctions that have brought us this far."