Efforts to secure the release of 15 Royal Navy personnel held by Iran will enter a "different phase" if diplomatic moves fail, Tony Blair has said.
Faye Turney was interviewed by the BBC last week
Downing Street said the UK could end up releasing evidence proving the group had not ventured into Iranian waters.
Foreign Secretary Margaret Beckett has called for their "speedy return".
One of the 15, Faye Turney told the BBC last week: "Sometimes you may be called upon, and when you do you've just got to deal with it and get on with it".
Meanwhile, the family of Ms Turney, from Shrewsbury, Shropshire, has said this is a "very distressing time" for them.
The BBC has been told the group are being held at an Iranian Revolutionary Guards Corps base in Tehran.
Iran says they were trespassing in Iranian waters when they were seized on Friday - but the prime minister said the group were in Iraqi waters under a UN mandate.
Mr Blair said the most important thing was the welfare of the eight sailors and seven marines from HMS Cornwall and securing their release.
The prime minister's official spokesman said Mr Blair's remarks about a "different phase" did not refer to any extreme diplomatic action, such as expelling Iranian diplomats from Britain or military action.
"We have been clearly stating that we are utterly certain that the personnel were in Iraqi waters.
"We so far have not made explicit why we know that, because we don't want to escalate this."
Britain's former ambassador to Iran, Sir Richard Dalton, said "different phase" could mean generating pressure on Iran from the international community.
"I expect he means that we shall have to step up criticism and generate additional international pressures on Iran," he said.
"It could be that they think that by dramatising the fact that these people were taken on an international mission while in Iraqi waters even further, will give Iran pause and give them a chance to rethink."
"These people have to be released," the prime minister told GMTV.
"What we are trying to do at the moment is to pursue this through the diplomatic channels and make the Iranian government understand these people have to be released and that there is absolutely no justification whatever for holding them.
"I hope we manage to get them to realise they have to release them. If not, then this will move into a different phase."
There is speculation that the capture was linked to the seizure of five Iranians by US forces in Iraq.
Mr Blair said the situations were "completely distinct" as any Iranian forces inside Iraq were breaching a UN mandate.
"In the end, it is a question really for the Iranian government as to whether they want to abide by international law or not," he said.
Captured female sailor Ms Turney said in an interview with the BBC last week: "My parents made sure that I was under no illusions that I could and can go to war at any time - that was the choice I made."
In a statement issued via the Ministry of Defence, sailor Ms Turney's family said they were grateful for the support they had received from everyone.
"While we understand the media interest in the ongoing incident involving Faye, this remains a very distressing time for us.
"We are grateful for the support shown to us by all personnel involved and appreciate it, but would request that our privacy is respected."
On Tuesday, an Iranian Foreign Ministry spokesman quoted by AP said those held were in good health, being treated in a humane fashion and Ms Turney had been given privacy.
The British foreign secretary said the UK was still pressing for consular access to the service personnel.
"If indeed they are being detained in reasonable circumstances then we can see no reason why they should not have contact with people from the British government," Mrs Beckett said.
An Iranian source has told BBC security correspondent Frank Gardner the Britons are being interrogated to find out if their mission was intelligence-gathering.
The source said the investigation involved examining tracking equipment to determine exactly where the crew was captured.
In order for the Britons to be released "every vested interest in Iran would need to be satisfied they had not deliberately entered Iranian waters, nor were they spying", the source added.