The British government has said it is suspending all contacts with Iran except negotiations to release the crew members.
The video also featured the lone female captive, Faye Turney, saying the boats had "trespassed" in Iranian waters, but British authorities said they believe her comments were coerced.
The British military has said its vessels were 1.7 nautical miles inside Iraqi waters when they were taken Friday, reported the Associated Press. It released GPS coordinates that it said proved the claims.
"Obviously, we trespassed into their waters," Turney said in the tape, 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."
The Iranian foreign minister said Turney would be freed Wednesday or Thursday.
The tape also showed what appeared to be the British crew sitting in an Iranian boat in open water.
A spokesman for British Prime Minister Tony Blair said before the tape aired that showing the crew on TV would be a breach of the Geneva Conventions.
"It's completely unacceptable for these pictures to be shown on television," he said, quoted the AP.
President Bush spoke to Blair about the standoff Wednesday, said White House deputy press secretary Dana Perino.
"The president fully backs Tony Blair and our allies in Britain," she said.
Iraq and Iran have never agreed on the ownership of waters near the mouth of the Shatt al-Arab waterway, where the British crews were seized, according to the AP.