Jill Carroll, 28, was wearing a headscarf and appeared in good health in the brief video aired by Al Rai TV on Thursday.
"I'm here with the mujahideen. I sent you a letter written by hand. I'm here, I'm fine. Please just do whatever they want," she said.
"Give them whatever they want as quickly as possible. There is very short time. Please move fast."
She said the video had been recorded on 2 February, but did not say what was in the letter that the TV station received along with the tape.
Jassem Boodai, the chairman of Al Rai TV, told Reuters that the station did not plan to broadcast the contents of the letter. "Because of the sensitive matters mentioned in it, we handed it over to Kuwaiti authorities," he said.
Carroll, a freelance journalist working for the Christian Science Monitor, was abducted in Baghdad on 7 January by fighters who also killed her Iraqi interpreter.
The newspaper said it wanted more information about the letter. "It is always difficult to see someone speaking under coercion and under these circumstances," Richard Bergenheim, editor of The Christian Science Monitor, said in a statement.
In constant contact
"We are seeking more information about the letter that Jill refers to in the video. We remain in constant contact with Jill's family and are still doing everything possible to obtain Jill's release," Bergenheim added.
Carroll had last appeared in a video aired on Aljazeera on 30 January in which she appealed to fellow Americans to press for the release of Iraqi women held by US-led forces.
Carroll has pleaded for jailed
Iraqi women to be released
The footage aired on Aljazeera carried a 28 January date stamp and a logo showing the name of the Revenge Brigades group.
Carroll had been on her way to a meeting with Adnan al-Dulaimi, a Sunni Arab leader whom she had intended to interview, when she was kidnapped.
Aljazeera had also aired a video tape showing Carroll on 17 January and said her abductors threatened to kill her if their demands were not met.
There has been a spate of kidnappings of Westerners in Iraq over the past few months after a lull during most of 2005. Four Christian peace activists - a Briton, an American and two Canadians - are still being held captive.