Falluja police chief Sabbir al-Janabi and two officers were also arrested with al-Jumaily when they tried to move members of their families to a nearby city to ensure their safety, Falluja police sources said.
Aljazeera has learned that al-Jumaily was arrested immediately after Friday prayers at a mosque in a village west of Falluja.
There were conflicting comments from the US military regarding al-Jumaily's arrest.
"We have not detained this gentleman," the US marines said in a statement.
However, Reuters later reported that a US military spokesman could neither confirm nor deny the arrest.
One of al-Jumaily's colleagues on the negotiating team with the Iraqi government told AFP earlier that al-Jumaily had been arrested.
"They arrested him after Friday prayers at a mosque in the village of Abu-Isa outside Falluja," Shaikh Abd al-Hamid Jadu said.
On Thursday, a delegation of city elders and leaders pulled out of talks with the Iraqi interim government, protesting against threats by the interim prime minister, Iyad Allawi, that the city would be invaded if it did not hand over Abu Musab al-Zarqawi and his supporters.
"We were taken aback by Allawi's comments since there was no mention of Zarqawi during the talks," one delegate, who gave his name as Abu Ahmad, said.
Allawi promised to attack if
al-Zarqawi was not handed over
"Allawi and his government will bear the responsibility of the spilling of Muslim blood in Falluja."
He said delegates were close to reaching a breakthrough in talks that would allow Iraqi forces to come back into the city before Allawi imposed "impossible conditions".
"Basically he was telling us that he did not want to negotiate, so we suspended the talks from our end," he said.
Allawi on Wednesday demanded that Falluja turn over al-Zarqawi or face a military invasion as he sought to recover the city from the grip of fighters ahead of national elections in January.