The clip, broadcast on Arabic-language television, also showed another serviceman and the only woman among the 15 British Navy personnel being held by Tehran.
The serviceman, identified as Nathan Thomas Summers, said he was aware that the incident was the second time since 2004 that British military personnel had entered Iranian waters.
"I know it happened back in 2004, and our government promised that it wouldn't happen again, and again, I deeply apologize for entering your waters," Summers said.
Britain denies that it violated Iranian territory in either case.
Summers also said that the captured service personnel were being treated humanely.
"Since we've been arrested in Iran, our treatment has been very friendly," he said. "We've not been harmed at all. They've looked after us really well. Basically, the food they've been serving us has been good, and I am grateful no harm has come to us."
Immediately afterward, Britain's Foreign Office denounced the video, saying it was "outrageous" to use British service personnel for "propaganda reasons."
Prime Minister Tony Blair today warned that if the Britons aren't released, Iran will become increasingly isolated by a world that abhors their capture and public exploitation:
"I really don't know why the Iranian regime keep doing this," Blair said. "I mean, all it does is enhance people's sense of disgust. Captured personnel being paraded and manipulated in this way doesn't fool anyone."
Britain Steps Up Diplomatic Pressure
So far, diplomatic efforts to end the crisis over Iran's seizure of the British sailors and marines have made little progress.
A British drive to get the UN Security Council to call for the immediate release of the crew fell well short of London's goals on March 29.
Instead, the Security Council expressed only "grave concern" and urged Tehran to provide "consular access" to the detainees.
Britain's ambassador to the UN, Emyr Jones Parry, summarized the outcome of Britain's efforts this way for reporters.
"No, I don't think we failed," Jones Parry said. " What is clear everyone in the council knows that these individuals were part of the multinational force, which is mandated actually by two Security Council resolutions, and I read those out to my colleagues in the council."
Security Council member Russia has appeared reluctant to back London in its dispute with Iran over whether or not the British sailors strayed into Iranian waters.
Russian Foreign Minister Sergei Lavrov said on March 29 that any naval or other forces operating in the Gulf region must "take into account the need not to aggravate the situation" there.
Britain maintains its ship was in Iraqi waters well outside of Iran's sea boundaries when it was seized by Iran's Islamic Revolution Guards Corps on March 23.
Engaging The EU
Meanwhile, Tehran has rejected Britain's efforts to involve the Security Council, saying the matter should be solved bilaterally with London. Tehran called the Security Council statement "not helpful."
British Foreign Minister Tony Blair said on March 29 that London will continue to try to ratchet up international pressure on Tehran, including through the EU.
The 27-nation bloc includes major trading partners with Iran, including Germany and Italy.
London got a sign of support from the EU on March 29 as the bloc's foreign policy and security chief, Javier Solana, called on it to condemn Iran's action.
"We have to condemn and condemn in a very clear manner and demand the immediate liberation of the U.K. soldiers taken by Iran," Solana said. "I think [we're] in agreement, in total agreement, after the debate of today, and we are, today, loud and clear."
Solana was speaking at the European Parliament in Brussels.
No Release For Female Sailor
British anger over the detentions have risen as Iran has reversed an earlier sign it might release the sole female sailor among the service personnel soon.
Iran said it now will not release Faye Turney because of London's efforts to involve the Security Council in the dispute.
Tehran released on March 29 a letter purportedly written by Turney saying she is being treated well but questioning the presence of coalition forces in Iraq.
"Isn't it time for us to start withdrawing our forces from Iraq and let them determine their own future?" the letter reads.
British Foreign Secretary Margaret Beckett said London has "grave concerns about the circumstances" in which such a letter was prepared and called any use of Turney for propaganda "outrageous and cruel."
Meanwhile, there are reports of some behind-the-scenes activity between Tehran and London to solve the crisis.
Reuters reports Britain's embassy in Tehran has received a formal note from the Iranian government regarding the detentions. The British Foreign Office has refused to divulge any of the details of the message.
Reuters also reports that Iranian state television said on TMarch 29 that President Mahmud Ahmadinejad will consider a request from Turkey to free the British female sailor, Turney.
Ahmadinejad has also called on Britain to apologize for what he says is an incursion into Iran's territorial waters.
(with material from Reuters, AP, AFP)