Baghdad's Interior Ministry said the dead included Arab and foreign fighters. Seven police commandos were also killed in the clashes on Tuesday in a deserted region 160km northwest of Baghdad, where sporadic fighting continued.
"Special forces in the Interior Ministry attacked a training centre ... and had a fierce battle with the terrorists, killing 84 of them," Sabah Kadhim, a spokesman at the Interior Ministry, said.
"Among the dead are Arab and foreign fighters, including Sudanese, Algerians and Moroccans, as well as other nationalities."
Officials said US helicopters and troops were called in as back-up during the battle, which lasted several hours.
The fighting came as politicians in Baghdad pushed on with talks to decide the make-up of a government more than seven weeks after the election, amid growing frustration among Iraqis.
The US military confirmed a battle had taken place and that US forces were involved, but a spokesman said he had no details on the numbers killed or captured.
US helicopters were called in as
back-up in Wednesday's raid
No US troops were wounded or killed in the fighting, he said.
"An early assessment of the site indicates a facility for training anti-Iraqi forces," Major Richard Goldenberg of the US 42nd Infantry Division said, using the US military's term for opposition fighters.
"Documentation at the facility indicates that some members of the AIF were foreign fighters."
Six police commandos were wounded, Goldenberg said.
Notices distributed by a group called the Islamic Army of Tikrit, a local anti-government group, said 11 fighters had been killed, while "many more" police commandos were slain.
In other incidents on Wednesday, two policemen were killed while defusing a roadside bomb in Baghdad and a family of four were killed in their car by a similar device, police said.
In Mosul a car bomber blew himself up near a US military patrol, but there were no reports of any injuries, apart from the bomber.
"Among the dead are Arab fighters, including Sudanese, Algerians and Moroccans, as well as other nationalities"
Iraqi Interior Ministry spokesman
The previous day Iraqi forces had detained 70 suspected anti-government fighters in the same city, the US military said.
Also on Wednesday, US forces launched a raid in Ramadi, arresting 12 people. The operation concentrated on neighbourhoods in the city centre.
In Haditha, a US patrol near the local general hospital was hit by an explosive device.
And in the Abu Ghraib suburb, west of Baghdad, Iraqi police found two beheaded bodies abandoned on the highway. The men were identified as members of the country's fledgling army.
Incidentally, on Tuesday a full-scale shootout had erupted between shopkeepers and armed gangs in Baghdad's al-Dura district.
Shopkeepers in the neighbourhood grabbed their guns and returned fire on three cars from which armed men sprayed their premises with bullets, interim Iraqi Defence and Interior Ministry officials said.
Three of the armed men were killed and another three were arrested after the clash near the Shia al-Sadr mosque, which left six civilians injured.