The two countries have been at loggerheads since Iran seized the sailors on March 23 in the northern Persian Gulf, but there have been few tangible signs of progress in the standoff.
On Monday Ali Larijani, secretary of Iran's Supreme National Security Council, said he believed that bilateral diplomacy could resolve the crisis quickly. Britain responded by saying it, too, would like early talks to end the dispute.
"We're not looking for confrontation over this, and actually the most important thing is to get the people back safe and sound. And if they want to resolve this in a diplomatic way, the door is open," Blair told a radio station in Scotland.
"The next 48 hours will be fairly critical," he said.
Oil prices tumbled more than $1 per barrel after Blair's comments on hopes that there may be a diplomatic end to the crisis, which has stoked fears that crucial oil supplies from the Persian Gulf could be hit.
British moves to get the international community to condemn Iran had angered Tehran, while Britain has criticized the parading of its military personnel on Iranian television, saying the broadcast admissions of guilt had been forced.
The dispute centers on where the sailors were when they were seized. Britain insists they were in Iraqi waters on a routine United Nations mission, but Tehran says they were in its waters.
Larijani said a "delegation" should determine whether the British trespassed.
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