Carroll had just left the office of Adnan Dulaimi, the head of the General Conference of the Iraqi People, on 7 January when she was abducted by armed men. The kidnappers set a deadline of Friday for killing her if authorities did not release women prisoners.
Aljazeera and Al Arabiya television stations aired the appeal from Carroll's father.
"I want to speak directly to the kidnappers of my daughter Jill, who could be fathers like me," Jim Carroll said on Aljazeera in remarks dubbed into Arabic.
"My daughter has no influence, she doesn't have the power to free anyone, she's just a journalist and an innocent person... Use her as a reporter to support your cause."
Dulaimi, one of Iraq's most influential Sunni leaders, on Friday called for her kidnappers to free Jill Carroll.
"Release this journalist who strived for Iraq, defended Iraqis and condemned the war in Iraq," Dulaimi told a news conference in Baghdad.
"Release this journalist who strived for Iraq, defended Iraqis and condemned the war in Iraq"
General Conference of the Iraqi People
Since 2003 more than 200 foreigners have been kidnapped in Iraq. Many of them have been killed.
Aljazeera aired a brief video on Tuesday night showing Carroll, 28, a freelance journalist working for the Christian Science Monitor. The group holding her said it would kill her if Iraqi women detainees were not released within 72 hours.
Iraqi officials said on Thursday the US military was freeing six women out of eight it was holding but that this was not linked to Carroll. A US defence official said the releases would not come soon, however.