Britain called the broadcast "completely unacceptable" and said it was concerned that the statements from sailor Faye Turney were coerced. The British government earlier released what it called proof the boat crews were seized in Iraqi waters, and said it was freezing all contacts with Iran except negotiations to release them.
Iran's foreign minister said Turney, the only female captive would be freed on Wednesday or Thursday, but British Prime Minister Tony Blair's office said it had received no confirmation of that.
The British military said its vessels were 1.7 nautical miles inside Iraqi waters when they were taken Friday, and it released what it said were the GPS coordinates that proved that.
Several hours later, Tehran broadcast the video on an Arabic-language satellite channel, along with a letter from Turney saying the sailors and marines were inside Iranian waters when they were captured.
"Obviously we trespassed into their waters," Turney said, sitting by herself against a floral curtain and smoking a cigarette.
"They were very friendly and very hospitable, very thoughtful, nice people. They explained to us why we've been arrested, there was no harm, no aggression," she said.
Turney, 26, was also shown eating with several fellow sailors and marines.
What appeared to be a handwritten note from Turney to her family said, in part, "I have written a letter to the Iranian people to apologize for us entering their waters."
The letter said Turney sent her love to her family and 3-year-old daughter.
"Please don't worry about me," the letter said. "I am staying strong. Hopefully it won't be long until I am home to get ready for Molly's birthday party with a present from the Iranian people."
Before the video was broadcast, a Blair spokesman said any showing of British personnel on TV would be a breach of the Geneva Conventions. The chief spokesman for the International Committee of the Red Cross declined to comment, saying the ICRC was not involved.
"It's completely unacceptable for these pictures to be shown on television," the Foreign Office said after the broadcast. "There is no doubt our personnel were seized in Iraqi territorial waters."
The statement also demanded that British diplomats be given immediate access to them as a "prelude" to their release.
The Foreign Office said it had "grave concerns" about Turney's state of mind when she spoke on video.
"I am very concerned about these pictures and any indication of pressure on or coercion of our personnel," said Foreign Secretary Margaret Beckett. She added that Britain had "comprehensively demonstrated today that our personnel were operating inside Iraqi territorial waters."
Blair told the House of Commons that "there was no justification whatever for their detention, it was completely unacceptable, wrong and illegal."
"We had hoped to see their immediate release, this has not happened. It is now time to ratchet up the diplomatic and international pressure in order to make sure the Iranian government understands its total isolation on this issue," Blair said.
Vice Adm. Charles Style told reporters that the Iranians had provided a position on Sunday, a location that he said was in Iraqi waters. By Tuesday, Iranian officials had given a revised position two miles east, placing the British inside Iranian waters, a claim he said was not verified by global positioning system coordinates.
"It is hard to understand a legitimate reason for this change of coordinates," Style said.
Style gave the satellite coordinates of the British crew as 29 degrees 50.36 minutes north latitude and 048 degrees 43.08 minutes east longitude, and said it had been confirmed by an Indian-flagged merchant ship boarded by the sailors and marines.
See Video Here: Iranian TV Airs Seized Sailor Interview
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