Tony Blair believes Iran wants to achieve an "early resolution" to the crisis over the Royal Navy crew through direct talks, Downing Street has said.
New pictures, from Fars News Agency, show the crew relaxing
A statement was issued after further UK contact with Iran, including directly with its chief negotiator Ali Larijani.
However, both countries continue to dispute whether the 15 crew were in Iran's waters when seized on 23 March.
Iranian President Mahmoud Ahmadinejad is expected to refer to the incident in a news briefing currently taking place.
So far there has been no official Iranian response to the UK's proposal for direct bilateral talks.
But Iran's parliament speaker Gholamali Haddadadel welcomed the "change in tone" from the UK.
According to Iran's official IRNA news agency, telephone talks between Mr Larijani and Mr Blair's chief foreign policy advisor Sir Nigel Sheinwald took place on Tuesday.
Downing Street's statement said: "The prime minister remains committed to resolving this by diplomatic means".
Meanwhile, reports say an Iranian envoy is expected to meet five Iranians detained by US forces in Iraq since January for the first time.
The report from IRNA, which was not confirmed by the US, comes amid suggestions that the navy crew's case could be improved by a release.
Iran says the five are diplomats, while the US claims the men were providing support to militants in Iraq.
Mr Larijani, of the Supreme National Security Council, hinted on Tuesday that a new phase in the talks with Britain had been started.
But Downing Street's statement came after Foreign Secretary Margaret Beckett had urged caution over hopes that the sailors and marines held by Iran may soon be freed.
UK VERSION OF EVENTS
1 Crew boards merchant ship 1.7NM inside Iraqi waters
2 HMS Cornwall was south-east of this, and inside Iraqi waters
3 Iran tells UK that merchant ship was at a different point, still within Iraqi waters
4 After UK points this out, Iran provides alternative position, now within Iranian waters
She said people had read a lot into remarks by the prime minister earlier in the day about talks with Iran entering a "critical" 48 hours.
Her comments were echoed by Home Secretary John Reid, who welcomed the contact with Iran but said there was no timescale for resolving the crisis.
"I can't put a time limit on this," he told GMTV. "The key thing here is that contact has been made."
On Tuesday, new photographs were released showing the Royal Navy crew.
The crew, from Plymouth-based HMS Cornwall, can be seen wearing tracksuits, smiling and playing chess.
IRANIAN VERSION OF EVENTS
1 Royal Navy crew stray 0.5km inside Iranian waters
2 Iran gives set of co-ordinates to back up their claims
3 According to seized GPS equipment, the Royal Navy crew had previously entered Iranian waters at several other points
4 Iran informs Britain of the position where the crew were seized, inside Iranian waters
Leading Seaman Faye Turney, 26, is not wearing a headscarf as she had in previous TV footage.
The naval personnel have been held captive since being seized by Iranian Revolutionary Guards in the northern Gulf last month.
Iran says they strayed into its territorial waters, but the UK maintains they were in Iraqi waters after returning from searching a merchant vessel.
Foreign Office Minister Lord Triesman has had talks with the Iranian ambassador in London eight times since the crew's capture.
It is understood that one area under discussion between the two countries is how future disputes over the contested Shatt al-Arab waterway may be avoided.