The statement, released Thursday, urged Iran to allow consular access to the Britons. It also said the Security Council called for an early resolution to the standoff, including release of the British personnel.
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Media reports say Russia had opposed including a British call for an immediate release of the captives.
Meanwhile, Iran says it will consider a Turkish request for Tehran to free the only woman among the 15 British personnel, Faye Turney.
Iranian state television reported that Turkish Prime Minister Recep Tayyip Erdogan made the request to Iran's President Mahmoud Ahmadinejad.
Iran initially said Turney could soon be freed but Iranian officials said Thursday her release was suspended because of "wrong behavior" by Britain.
British Foreign Secretary Margaret Beckett said attempts by Iran to use Turney as propaganda are -- quote -- "outrageous and cruel."
Iran's embassy in London released a second letter Thursday, purportedly from Turney, that says the 15 Britons had entered Iranian waters. The letter also calls for Britain to withdraw its troops from Iraq.
Britain says satellite positioning information shows that its sailors were in Iraqi waters when they were captured last Friday.
Iran says Britain must acknowledge the 15 were in Iranian waters if it wants to resolve the crisis.
Some information for this report provided by AP, AFP and Reuters.