Foreign Secretary Margaret Beckett summoned the Iranian ambassador over the incident, which risks inflaming already mounting tension between the Islamic republic and the West over Tehran's nuclear plans.
"The British government is demanding the immediate and safe return of our people and equipment," the ministry said, underlining that the sailors had been in Iraqi waters.
A senior Navy commander said he hoped the capture - involving sailors from HMS Cornwall - was a "misunderstanding," while admitting that the area where they were detained, in the Shatt al-Arab waterway, was disputed.
"There is absolutely no doubt in my mind that they were in Iraqi territorial waters. Equally, the Iranians may well claim that they were in Iranian territorial waters," Commodore Nick Lambert, commander of a coalition taskforce operating in the area, told the BBC.
"I hope we find that this is a simple misunderstanding at a tactical level." A BBC television correspondent on board HMS Cornwall said that the group had been seized at gunpoint, but this information could not immediately be confirmed.
It is not the first time British sailors have been seized by Iran in the Shatt al-Arab, which runs into the Gulf between Iraq and Iran, but it comes amid a fraught diplomatic climate as the West seeks to press Tehran to curb its nuclear programme.
The abduction came as the United Nations Security Council prepared to vote on new sanctions against Iran, probably on Saturday. In Friday's incident, which occurred about 10:30 am local time, the defence ministry said that "15 British naval personnel, engaged in routine boarding operations of merchant shipping in Iraqi territorial waters ... were seized by Iranian naval vessels."
The 15 had completed a successful inspection of a merchant ship when they and their two boats were surrounded and escorted by Iranian vessels into Iranian territorial waters, the ministry said in a statement.
"We are urgently pursuing this matter with the Iranian authorities at the highest level and on the instructions of the Foreign Secretary, the Iranian ambassador has been summoned to the Foreign Office. A ministry spokesman declined to give further details, but underlined that the British navy was boarding merchant ships in Iraqi waters in support of UN Security Council resolution 1723.
"Typically what happens is that we would send a couple of inflatables," he said. "It was a routine boarding operation in support of the UN resolution. "Normally what would happen is that we have the Navy ships monitoring vessels going in and out of the area, so we would call them up on the radio and go through a simple list of checks and if there's anything that's not right, they send out two boats of naval personnel to board it.
"They check the cargo and see if the boat needs any assistance," he said. British naval boats routinely patrol the Shatt al-Arab to clamp down on smugglers operating between Iraq and Iran.
In June 2004, six British marines and two navy sailors were detained for three days in Iran after being seized during another routine operation. They were paraded blindfold on television and forced to apologise for their "mistake."
On that occasion Iran insisted that the British boats, which it has not yet returned, were intercepted only after they entered Iranian waters on the Shatt al-Arab.
IRAN QUIET ON DETENTION REPORT Iran was silent on Friday over reports that Iranian naval vessels had arrested 15 British sailors in Gulf waters earlier in the day. Officials could not be reached for comment during what are Iranian New Year celebrations, and state media made no reference to the matter.
The British defence ministry said 15 British naval personnel, engaged in routine boarding operations of merchant shipping in Iraqi territorial waters, had been seized on Friday morning. British Foreign Secretary Margaret Beckett has summoned the Iranian ambassador, demanding the sailors' immediate release and urgent clarification from Tehran.
The incident comes amid mounting tension between the Islamic republic and the West over Tehran's nuclear programme, which the West fears could be used to develop atomic weapons. The Iranian navy launched military exercises in the Gulf on Thursday in a display of the Islamic republic's "power and defence capability."
Iran accuses British forces based across the border in southern Iraq of backing separatist ethnic Arabs in Iran's oil-rich Khuzestan province. London denies the allegation. In June 2004, six British marines and two sailors were detained for three days in Iran after a routine operation. They were paraded blindfold on television and forced to apologise for their "mistake."
On that occasion Iran insisted that the boats - which it has not yet returned - were intercepted only after they entered Iranian waters on the Shatt al-Arab, the waterway that divides Iran and Iraq.