The British diplomatic initiative received support from the US president on Saturday who said that Iran's seizure of the sailors was "inexcusable behaviour".
"It is Iran's responsibility to find a quick solution"
Emkay, Auckland, New Zealand
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"It's a serious issue because the Iranians took these people out of Iraqi waters," George Bush said at his mountain retreat in Camp David, Maryland.
"And it's inexcusable behaviour and I strongly support the Blair government's attempts to resolve this peacefully."
He rejected suggestions that Washington could help in the eight-day-old standoff by freeing five Iranians captured by US forces in northern Iraq in January.
Earlier on Saturday, Iran's president said the British governnment was not following "the legal and logical way" over the case.
Mahmoud Ahmadinejad was quoted as saying by the state radio report: "After the arrest of these people, the British government, instead of apologising and expressing regret, over the action taken, started to claim that we are in their debt and shouted in different international councils.
"But this is not the legal and logical way for this issue."
A diplomatic note from Iran to Britain released on Friday condemned the "illegal act" by British naval staff and called on the UK to accept responsibilty for the standoff.
Also on Friday, Iranian television broadcast footage of three of the British naval personnel in which one of them apologised for entering Iranian waters without permission.
Britain has insisted that the naval personnel were in Iraqi waters when they were detained.
Iran's ambassador to Moscow has meanwhile denied saying that the British naval personnel held by Iran may face trial for illegally entering Iranian waters.
Gholam Reza Ansari said a Russian television station had mistranslated his remarks.
"The network has made a mistake in translating the comments about detained British personnel and has reported the possibility of their trial," he told the Iranian state news agency IRNA.
Ansari was earlier quoted by IRNA as telling Russian television channel Vesti-24: "It is possible that the British soldiers who entered into Iranian waters will go on trial.
"The legal phase concerning these British soldiers has started and if charges against them are proven, they will be punished."
And in a related development, Terry White, a former British hostage who was held captive for almost five years in Lebanon from 1987 to 1991, has offered to mediate in resolving the crisis.
Speaking to Al Jazeera, White expressed his readiness to visit Iran to persuade Tehran free the seized personnel.