But conflicting reports have emerged over whether or not the ousted Iraqi president is joining the hunger strike.
"It appears that some of the other 11 high-value detainees have been rejecting food, although they continue to snack and to take on liquids," Lieutenant Colonel Barry Johnson, deputy director of detainee operations in Baghdad, said on Sunday.
"We're trying to ascertain who is turning their food back and why," he said.
Johnson said those who had rejected food began doing so on Saturday, but some had also eaten on Sunday morning.
"There are a lot of conflicting reports about what they have eaten and when," he said, denying Saddam, who is held separately, was among those not eating.
Lawyer Arif Badia, who represents former deputy prime minister Tariq Aziz, said he had heard from a lawyer for another former Baath party official that most of those on the US military's 55 most wanted list and in captivity were on hunger strike.
Former Iraqi vice-president Taha
Ramadan is on hunger strike
"Taha Yasin Ramadan's lawyer told me that Ramadan went on hunger strike along with several other prisoners to protest their illegal detention," Badia said, adding that Ramadan's lawyer had seen his client on Saturday. Ramadan is the former vice-president.
Badia, who said he had yet to meet Aziz in detention, denied saying Saddam was among those refusing to eat, as some reports suggested.
The protest was about a lack of access to defence lawyers and because the detainees are concerned about their status once a new Iraqi government is in power after elections scheduled for 30 January.
"They heard that they are going to be handed over after the elections to an Iraqi government they will not recognise," Badia said.
Johnson said Aziz was among those who had been turning down food. All 12 so-called high-value detainees appeared in court in July this year to be informed of general charges against them, but have yet to be tried.
While they are in US physical custody, legally they are in Iraqi hands. The US military has not said what will happen to their physical custody if a new Iraqi government is elected next month.
"Saddam is not on a hunger strike. He ate all of his scheduled meals today"
US military spokesman
A US military spokesman in Baghdad said: "Saddam is not on a hunger strike. He ate all of his scheduled meals today."
Iraq's ousted president, who was taken ill earlier this year and treated for a prostate infection, was captured by US troops on 13 December 2003 near his hometown of Tikrit in northern Iraq.
He has been visited by the International Committee for the Red Cross several times at his secret detention facility, believed to be close to Baghdad airport, but has not seen a lawyer.
His Jordan-based lawyers say they have been denied permission to visit him.