The 28-year-old freelancer for the Christian Science Monitor was kidnapped in Baghdad on 7 January and last seen in a videotape broadcast this month by Alrai, the private Kuwaiti television station.
Jassem Boudai, the station owner, said the kidnappers set a Sunday deadline for US and Iraqi authorities to meet their demands or they would kill her.
The kidnappers had demanded the release of all women detainees in Iraq but Boudai indicated the group had provided more specific conditions which he refused to reveal.
On Sunday, an Iraqi Interior Ministry official said an extensive search was underway for Carroll but had so far failed to find her.
"Our forces raided some suspected places, but she was not there," Major Falah al-Muhammedawi said.
"We are watching the situation closely."
Also on Sunday, Aljazeera broadcast a tape it received from the family of Canadian hostage James Loney 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.
"James is a loving, compassionate, selfless man"
Relative of James Loney
She did not say what her relation to Loney was, but may have been his sister-in-law since she said her husband and his relatives were scared for their brother.
The woman called for the release of Loney and the others so that they could return to their families and continue to carry out their humanitarian duties in Iraq.
Loney was among four members of the Christian Peacemaker Teams seized on 26 November in Baghdad by the previously unknown Swords of Righteousness Brigade.
The other three are a Canadian, an American and a Briton.
The woman said the hostages highly appreciated the Iraqi people, whom Loney never hesitated to support.
She said she was grateful for efforts by Muslim and Christian clerics to secure the release of the hostages.
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 Shia 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 curfew and vehicle bans in the capital have calmed tempers but the situation remains tense.
Three Iraqi journalists were slain on Wednesday while covering the shrine bombing.
Organisations as varied as Hamas, the Bush administration, the Committee to Protect Journalists and the student newspaper at the University of Massachusetts have called for Carroll's release.