Carroll appeared in the black-and-white video wearing an Islamic veil, sitting in a chair in front of a wall with a large floral design. She spoke to the camera in a firm voice, without weeping.
"I am here. I am fine. Please just do whatever they want, give them whatever they want as quickly as possible," she said, saying she was speaking on Feb. 2. "There is a very short time. Please do it fast. That's all."
The video was aired on Al Rai TV, a private Kuwaiti channel, unlike two previous videos of Carroll issued by her captors, which were handed over to the more widely watched Al-Jazeera.
The video was delivered earlier Thursday to Al Rai's headquarters in Kuwait, Hani al-Srougi, an editor at the station, told The Associated Press. It was accompanied by a letter written by Carroll, which the station is holding. He would not give the contents of the letter.
In the tape, Carroll mentions the letter and suggests that her captors issued a letter in her handwriting previously. It was the first report of any letters from Carroll.
"I am with the mujahadeen (holy warriors). I sent you a letter written by my hand, but you wanted more evidence, so we are sending you this letter now to prove I am with the mujahadeen," she said.
Nearly 70 U.S. officials are working non-stop to figure out who has Carroll, reports CBS News correspondent Kimberly Dozier, and Iraqi forces are staging raids almost every night trying to track her down. Carroll's family has said that they are grateful that so many people are working to free her, Dozier adds.
The 28-yar-old Carroll, who worked freelance for The Christian Science Monitor, was abducted on Jan. 7 in Baghdad. Her captors, calling themselves the Revenge Brigades, demanded the release of all Iraqi women prisoners held in U.S. and Iraqi jails.
On Jan. 17, Al-Jazeera aired a video released by the Revenge Brigades showing Carroll, her head bare, and her long straight brown hair parted in the middle, setting a Jan. 20 deadline for the demands to be met or she would be killed.
The deadline passed with no word on her fate on Jan. 30, showing Carroll, now in an Islamic veil, weeping and speaking to the camera. She appealed again for the Iraqi female prisoners' release, Al-Jazeera reported.
The Qatar-based Al-Jazeera did not play the audio for either video, saying it was too wrenching for viewers, though at one point, Carroll's cracking voice can be heard in the second video, saying "...hope for the families..."
Al Rai played the audio in Thursday's video.
In Baghdad, a U.S. Embassy spokesman Dennis Culkin said Thursday that American authorities routinely do not comment on tapes especially before they have been authenticated.
The reporter's parents have made repeated televised pleas for their daughter's release. A Washington-based American Islamic advocacy group flew to Baghdad to drum up support for Carroll, and Islamic leaders from Iraq to Paris have called for her freedom.
Carroll grew up in Ann Arbor, Mich., and graduated from the University of Massachusetts. She worked as a reporting assistant for The Wall Street Journal before moving to Jordan and launching her freelance career in 2002, learning Arabic along the way.
Ann Cooper with the Committee to Protect Journalists told CBS News correspondent Byron Pitts that Carroll kept a low profile in Iraq, and tried to blend in by traveling without much security. Cooper said there has been a debate about which is safer – to travel under the radar or to report with heavy security – but the recent attack in which ABC News anchor was injured shows that
Some 250 foreigners have been taken captive since the 2003 U.S.-led invasion that toppled Saddam Hussein, and at least 39 have been killed.