( CNN ) - Iran's foreign minister says British officials will be allowed to meet with 15 detained sailors and marines, but must acknowledge that the service members entered Iranian waters in order to resolve the standoff.
"Admitting the mistake will facilitate a solution to the problem," Manouchehr Mottaki told The Associated Press late Wednesday night in Riyadh, Saudi Arabia, where he was attending an Arab summit.
Mottaki's statement came on a day of escalating tensions, highlighted by an Iranian video of the detained Britons that showed the only female captive saying her group had "trespassed" in Iranian waters.
The British Ministry of Defence has given what it said was proof the British ship HMS Cornwall, which was carrying the sailors and marines, never strayed into Iranian waters.
The global positioning system on the ship proves the vessel was "clearly" 1.7 nautical miles inside Iraqi waters and that the boat was "ambushed" by the Iranian forces, British Vice Adm. Charles Style said.
A map with coordinates that Iran provided on Saturday "turned out to confirm [the sailors] were in Iraqi waters," and Iraq has supported that position, Style said.
Iran later provided a second set of coordinates on Monday that placed the vessel inside Iranian waters, Style said. Those coordinates placed the ship "over two nautical miles" from the position shown by the HMS Cornwall and confirmed by the merchant vessel the British personnel had boarded when captured.
The "change of coordinates," Style said "is hard to legitimate."
On Wednesday, the Iranian Embassy in London said in a statement that British personnel had made an incursion of 0.5 kilometers ( 0.3 miles) into Iranian territorial waters.
The row over the location of the British personnel when captured on March 23 intensified Wednesday when images of them in detention appeared on Iranian television.
The female British soldier who was detained along with 14 male sailors and marines in the Persian Gulf last week said her crew "trespassed" into Iranian waters.
"Obviously we trespassed into their waters," Faye Turney said in video broadcast by Alalam, an Iranian Arabic-language network.
"They were very friendly, very hospitable, very thoughtful, nice people. They explained to us why we'd been arrested. There was no aggression, no hurt, no harm. They were very, very compassionate," Turney said.
It was not known when the videotape was shot, or whether Turney, 26, was able to speak freely.
Turney -- who holds the rank of leading seaman, roughly equivalent to a petty officer first class in the U.S. Navy -- appeared to be in good physical condition and wore a black scarf to cover her hair. (Read Turney's profile)
In other scenes, she was shown smoking a cigarette as she spoke with someone off camera.
Mottaki, Iran's foreign minister, told CNN Wednesday that Turney would be released soon.
Alalam also broadcast video showing some of the other British detainees eating with Turney. All appeared healthy and unharmed. It was not known when that video was taken either.
The video broadcasts met outrage by the British government.
A spokesman for Britain's Foreign Office said it was "completely unacceptable for these pictures to be shown on television, given the potential distress to their [the sailors'] families."
British Foreign Secretary Margaret Beckett said she was "very concerned about these pictures and any indication of pressure on or coercion of our personnel." They "were carrying out a routine operation in accordance with international law and under a United Nations resolution in support of the Iraqi government," she added.
Britain would cut off all bilateral diplomatic business with Tehran -- excluding discussions about the detainees -- until they were released, she announced earlier Wednesday.
Beckett said that even if the ship had strayed into Iranian waters, "under international law, warships have sovereign immunity in the territorial sea of other states."
"The very most Iran would've been entitled to do if they considered our boats were breaching the rules on innocent passage would've been to require the ship to leave their territorial waters immediately," the foreign secretary explained.
Alaedin Boroujerdi, a member of the Iranian parliament and head of the National Security and Foreign Policy Commission, warned Britain that "the days of bullying are over."
"Threats of disrupting trade and economic relations will only make matters worse and more complicated," he told the Fars News Agency.
The Iranian government was still refusing to give British officials information on exactly where the Britons were being held and was denying consular access to them, Beckett said.
Iranian officials said they will allow British diplomats to see the detainees once an investigation is completed.
Iran also released a letter it said was written by Turney to her parents. The letter was handed to the British ambassador to Iran in Tehran on Wednesday, the state-run news agency reported.
"We were out in the boats when we were arrested by Iranian forces as we had apparently gone into Iranian waters. I wish we hadn't because then I'd be home with you all right now. I am so sorry we did, because I know we wouldn't be here now if we hadn't," the letter said.
CNN cannot confirm that Turney wrote the letter or, if she did, whether she did so under duress.
The television station broadcast video of what appeared to be a handwritten letter, signed "Faye."
"I want you all to know that I am well and safe. I am being well looked after. I am fed 3 meals a day and have a constant supply of fluids," the letter said.
