Iran has offered to let UK officials visit the 15 Royal Navy personnel who were captured in the Gulf on Friday.
Iran's foreign minister also said the only woman being held, Faye Turney, who has been interviewed on Iranian state television, could be released.
But he said the stand-off would be resolved only if the UK stated that the sailors and marines had been in Iranian waters last Friday, which it denies.
UN Secretary-General Ban Ki-moon has held talks with Iran on the issue.
His spokesman said the detention was one of the issues discussed during a meeting with Iranian foreign minister Manouchehr Mottaki at a summit of Arab leaders in the Saudi Arabian capital, Riyadh.
The European Union foreign policy chief Javier Solana said he had spoken briefly to Mr Mottaki at the summit and reiterated the EU's call for an end to the "illegal" detention.
The Foreign Office said it was waiting for further details on possible consular access, and that no official offer had yet been made by Iran.
In the Iranian TV interview, Leading Seaman Turney, 26, said the group had been seized in the Gulf because "obviously we trespassed" in Iranian waters.
She said her captors had been friendly and the 15 personnel, who were all based on HMS Cornwall in the Gulf, were unharmed.
The video showed a letter, said to have been written by Leading Seaman Turney, who is from Shrewsbury, to her parents in which she admitted that the navy personnel had "apparently" crossed into Iranian waters.
The pictures also featured the 14 servicemen seized along with Leading Seaman Turney.
Foreign Secretary Margaret Beckett said: "I am very concerned about these pictures and any indication of pressure or coercion of our personnel who were carrying out a routine operation in accordance with international law and under a United Nations Resolution."
Defence Secretary Des Browne said it was "completely unacceptable to parade our people in this way".
Former RAF pilot John Nichol, who was put on television by the Iraqis after being shot down in the first Gulf War, told BBC Radio 4's Today programme he had "no doubt" Leading Seaman Turney had been told what to say.
"It is a very difficult position - and she's in an unenviable position where she has to try to placate the people that have captured her and try to keep the whole group safe," he said.
Iran has not disclosed where the service personnel are being held but the BBC has been told they are at a military base in Tehran.
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
Tony Blair has said it is time for the UK to "ratchet up" pressure on Iran.
Deputy Chief of the Defence Staff, Vice Admiral Charles Style, has produced data which he said proved the boarding party was 1.7 nautical miles inside Iraqi waters.
The Ministry of Defence also released a photograph of a handheld global positioning satellite device in HMS Cornwall's Lynx helicopter as it flew over the merchant vessel which was searched by the group before they were seized.
Ed Owen, who was an advisor to Jack Straw during his time as foreign secretary, told BBC Radio Five Live he thought Iran had deliberately engineered the incident.
"There are people in the Iranian regime who believe that the way to address what they regard as the dangers of the West, as well as expanding Iranian influence, is to confront the West," he said.
The Iranian embassy in London said the Britons had been 0.5 km inside Iranian territorial waters.