Mary Beth Carroll told CNN that video images gave her hope that her daughter is alive but also have "shaken us about her fate."
"I, her father and her sister are appealing directly to her captors to release this young woman who has worked so hard to show the sufferings of Iraqis to the world," she said.
Carroll, a 28-year-old freelance journalist for The Christian Science Monitor who grew up in Ann Arbor, Mich., was abducted Jan. 7.
New images showing Carroll surrounded by armed and masked hostage-takers in Iraq were aired Thursday by an Arab satellite TV station.
Qatar-based Al-Jazeera aired about 20 seconds of silent footage showing 28-year-old Jill Carroll sitting and talking to a camera in one shot and surrounded by three insurgents with their faces covered by traditional Arab scarves in another.
The report said the video included a threat to kill Carroll in 72 hours unless U.S. authorities agreed to release all women detainees in Iraq.
One of the insurgents was shown standing behind a seated Carroll in what appeared to be a room of a house and reading a statement.
Meanwhile, Iraq has asked U.S. authorities to release six of the eight Iraqi females in military custody but not as part of a bid to free a kidnapped American woman journalist, a government official said Thursday.
The U.S. military confirms there are eight women in custody in Iraq. A White House official told CBS News that Carroll's plight is dire and underlined that the U.S. never negotiates with terrorists.
Carroll said her daughter has always shown the highest respect for the Iraqi people and their customs in her reporting.
"We hope that her captors will show Jill the same respect in return," she said. "Taking vengeance on my innocent daughter, who loves Iraq and its people, will not create justice."
Carroll asked that her daughter's captors find a way to contact her to discuss her daughter's release.
"We call upon you to ensure that Jill is returned safely to her family, who needs her and loves her," she said.
"We're taking every step we can think of to take," David Cook, the Washington bureau chief of the Monitor, said on CBS News' The Early Show. "It seems so unjust that someone who has been such a careful, unbiased, sensitive reporter could be murdered for that kind of public service."
Cook told Early Show co-anchor Julie Chen he's hopeful Carroll will be released.
"There have been developments, we've had some positive developments in terms of statements from politicians in Iraq, from clerics in Iraq, so we take some comfort from that. But there's much more to be done," Cook said. "The clock is ticking, and we need to keep working to get her out."
Two of the most powerful Muslim organizations worldwide are calling for her release, reports CBS News correspondent Elizabeth Palmer.
Insurgents in Iraq, mainly Sunni Arab militants, have kidnapped more than 240 foreigners and killed at least 39 of them. Hundreds, perhaps thousands, more Iraqis have been abducted either by insurgents or gangs seeking ransoms.
The fate of two engineers, believed to be Kenyans and working for Iraqi cell phone company Iraqna, was still unknown after they went missing and were feared kidnapped in an ambush of their security convoy in Baghdad on Wednesday.
The U.S. military said a government commission reviewing cases of Iraqi detainees recommended to U.S. authorities on Monday that six women be released.
An official from the Human Rights Ministry, which sits on the commission along with representatives of the Defense and Justice ministries, said the call was not made in response to demands from Carroll's kidnappers, who gave authorities until Friday night to free the women.
"There was no outside pressure on the commission" to release the women, said the official who declined to be identified further because he feared reprisal from insurgents.
"This recommendation came after we studied the women's files provided by American military and we recommended their release," the official added.
U.S. officials have refused to comment on whether any of the women were set to be released.
Carroll's translator — although she speaks Arabic she used a translator — told police just before he died that the abduction took place when he and Carroll were heading to meet Adnan al-Dulaimi, head of the Sunni Arab Iraqi Accordance Front, in the Adel section of the city. The neighborhood is dominated by Sunni Arabs and is considered one of the toughest in Baghdad.
Her driver, who survived the attack, said after Carroll and her party had waited 25 minutes for the politician to show up for the interview, they gave up and were leaving when their car was stopped.
"It was very obvious this was by design," the driver, who asked not to be identified, told the Monitor. "The whole operation took no more than a quarter of a minute. It was very highly organized. It was a setup, a perfect ambush."