The captives - two brothers and their cousin - said on a video posted on the internet that they were hired by a Jordanian firm to maintain a swimming pool at the US base near the capital Baghdad.
The video showed their apparent shooting outdoors by armed men.
"I advise Iraqis not to work with Americans. I regret what I did," said one blindfolded hostage in the video posted on the group's website.
The tape's authenticity could not be verified immediately.
The organisation, one of the main Sunni Muslim groups, has claimed responsibility for attacks against US forces and the Iraqi government and has killed several captives.
Also on Monday the Philippines urged all its nationals to leave Iraq after a Filipino man working at a US-run military camp was shot dead in downtown Baghdad.
Rey Torres, who worked as a security guard and driver for a Qatari subcontractor at Camp Victory, was attacked in Baghdad on Sunday night shortly after he ended his shift, the foreign department there said.
There were no other details of the attack on Torres, the first Filipino to be killed in Iraq since Manila withdrew its small contingent of soldiers and police in July last year to save the life of another driver, Angelo de la Cruz, who had been seized by fighters.
A travel ban was imposed after
de la Cruz's seizure
Foreign Secretary Roberto Romulo issued an urgent appeal to Filipino workers to leave Iraq immediately.
There are at least 6000 Filipinos in Iraq according to Philippine government estimates, even though Manila banned travel to that country after the de la Cruz incident.
Meanwhile, US forces surrounded the al-Zaidan and al-Radwaniya areas west of Baghdad, Aljazeera learned.
The forces have closed all entrances and exits of the two areas, launching a vast search operation.
A resident of the area, Abu Bakr al-Zawbai, told Aljazeera the area was being targeted due to the high number of attacks against US forces there.
"Khan Dhari Zaidan and al-Radwaniya areas surround Abu Ghraib prison which has been subject to some successful operations," he said. "Therefore, US and Iraqi forces have surrounded these two areas.
"US forces, backed by helicopters, have been heavily deployed in the area. Sounds of helicopters can be heard hovering over it," he added.
He also called on all human rights groups to pay attention to these areas.
"People have stayed at their homes as they believe a vast operation will be carried out soon," he said.
"This area has lost a lot of its people and witnessed severe damage to its properties, only because it hosts Abu Ghraib prison."