Top diplomats from Iran and the United States held "substantive" talks Wednesday aimed at speeding up negotiations for a nuclear deal, with US Secretary of State John Kerry heading back for a surprise new round.

State Department officials said the talks with Kerry and his Iranian counterpart Mohammad Javad Zarif had ended about 6:00 pm (1700 GMT) after about five hours.

But 90 minutes later the two men suddenly held another surprise meeting at an upscale Geneva hotel, a senior State Department official said.

The second meeting lasted over an hour, concluding shortly before 9:00 pm (2000 GMT), but it remained unclear what it focused on.

The two men are seeking to break a stalemate which has caused them to miss two previous deadlines for a full agreement to rein in Iran's suspect nuclear programme.

Zarif told reporters Wednesday's talks were "important."

"I think it will show the readiness of the two parties to move forward to speed up the process."

But asked if there would be a comprehensive deal by the new July 1 deadline, he remained cautious, replying: "We'll see."

Kerry and Zarif even moved their discussions outside at one point, leaving the hotel for a brief stroll around Geneva city centre, causing some consternation for their security teams.

After the first meeting finished Wednesday, a senior State Department official said: "They had substantive meetings for approximately five hours today and they discussed a broad range of issues with a small group of staff from each side."

Kerry then briefed his negotiators before lower level US-Iran bilateral talks here on Thursday, ahead of Sunday's discussions with the whole P5+1 group -- Britain, China, France, Germany, Russia and the United States.

Past negotiations have stumbled reportedly over Iran's insistence that it retain the right to enrich some uranium -- which can in some cases be used to make an atomic bomb -- for what it says is a peaceful civilian nuclear programme.

There has also been disagreement over global sanctions, with Tehran calling for an end to an iron-clad regime which has crippled Iran's economy, while the US has insisted on a temporary, gradual suspension.

Negotiators have been tight-lipped about their differences and Zarif would not go into detail when asked about the thorniest matters still clouding the talks.

"All issues are hard until we resolve them and all issues are easy if you resolve them," he told reporters travelling with Kerry.

- Clock ticking -

The top US diplomat, who was accompanied to Wednesday's talks by his chief negotiators Wendy Sherman and Bill Burns, told reporters earlier this week that he hopes to "accelerate the process to make greater progress."

Diplomats fear time may be running out after two earlier deadlines for a deal were missed.

The new Republican-controlled Congress is already considering a bill which would slap new sanctions on Iran despite attempts by the Obama administration to hold them off.

Washington's UN envoy Samantha Power warned Monday that "imposing new sanctions will almost certainly end a negotiations process that has not only frozen the advance of Iran's nuclear programme, but that could lead us to an understanding that would give us confidence in its exclusively peaceful nature."

Zarif, who was set to meet German Foreign Minister Frank-Walter Steinmeier in Berlin Thursday and his French counterpart Laurent Fabius in Paris Friday, has meanwhile repeatedly stressed that Iran is not seeking to obtain a nuclear weapon.

He told Iranian television earlier that "we have arrived at the stage where the other party must take decisions so we can go forward."

"New proposals must be put forward. We are ready to discuss all the issues, but we will have to see if the other side is ready," he said.

Under an interim deal between world powers and Tehran in force since January 2014, Iran agreed to limit its uranium enrichment.

In return, Iran received limited relief from a network of global sanctions, obtaining about $7 billion (over 8 billion euros) from more than $100 billion in oil revenues frozen in bank accounts around the world.