"The Ministry of Interior said that she is alive and that they have information with regard to where she might be held," Khalilzad told FOX News.
"The minister announced today that he is optimistic about her release," he said.
Khalilzad didn't say how the Interior Ministry knew about Carroll's well-being.
"We are doing all we can to help bring about her release and we'll persist with that," Khalilzad said.
Iraqi police conducted raids in search of Carroll on Sunday, the deadline set by her captors for the United States to meet their demands, but the day passed without word on whether her captors carried out their threat to kill her.
The 28-year-old freelancer for the Christian Science Monitor was kidnapped Jan. 7 in Baghdad and was last seen in a videotape broadcast Feb. 9 by the private Kuwaiti television station Al-Rai.
Station owner Jassem Boudai said then that the kidnappers had set Feb. 26 as the deadline for U.S. and Iraqi authorities to meet their demands or they would kill her.
The kidnappers, a formerly unknown group calling themselves the Revenge Brigades, have publicly demanded the release of all women detainees in Iraq, but Boudai indicated the group provided more specific conditions that he refused to reveal.
On Sunday, an Iraqi Interior Ministry official said an extensive search was under way for Carroll.
"Our forces raided some suspected places, but she was not there," Maj. Falah al-Mohammedawi said. "We are watching the situation closely."
The Bush administration, Hamas, the Committee to Protect Journalists and the student newspaper at the University of Massachusetts have called for Carroll's release.
A woman who answered the phone Sunday morning at Carroll's mother's house said the family had no new information and politely declined comment.
David Cook, the Monitor's Washington bureau chief, echoed that sentiment and reserved comment. On Saturday, he said: "We know our journalistic colleagues will understand why we need to exercise great care in commenting on Jill's situation."
Also Sunday, the Arabic-language Al-Jazeera satellite channel broadcast a tape it received from the family of another hostage, James Loney of Canada, appealing for his release and that of three colleagues abducted with him in Baghdad last November.
"James is a loving, compassionate, selfless man," said a woman relative who appeared on the tape. She did not say what her relation to Loney is, but may have been his sister-in-law since she said her husband and his relatives were scared for their brother.
Loney was one of four members of the Christian Peacemaker Teams seized Nov. 26 in Baghdad by the previously unknown group calling itself the Swords of Righteousness Brigade. The other three are a Canadian, an American and a Briton.
The woman said she was grateful for efforts by Muslim and Christian clerics to secure the release of the hostages.
Iraqi television has aired three videos of Carroll since her kidnapping. In the first, shown on Al-Jazeera on Jan. 17, her abductors threatened to kill her unless the United States freed female prisoners in Iraq.
The second and third videos were broadcast without sound. In the second, aired on Al-Jazeera, the broadcaster said Carroll asked for the release of the female prisoners.
The third video was aired on Al-Rai.
Since Wednesday, Iraqi security officials have been preoccupied with the grave security crisis that erupted when two bombs destroyed the golden dome of the Askariya shrine in Samarra, which is revered by Shiite Muslims.
The destruction of the site triggered a wave of reprisal attacks against Sunni mosques and clerics and pushed the country to the brink of civil war. Stepped up security — including daytime curfews and vehicle bans in the capital — have eased tensions somewhat.
Three Iraqi journalists were slain Wednesday while covering the shrine bombing.
The Associated Press contributed to this report.