US Secretary of Defence Donald Rumsfeld would not directly confirm or deny the report when asked about it in several TV interviews, saying only that "we talk to people all the time".
The Sunday Times newspaper in London said the commanders "apparently came face to face" with four American officials during meetings on 3 June and 13 June at a summer villa near Balad, about 40km north of Baghdad.
The report, which quoted unidentified Iraqi sources, said the groups at the first meeting included Ansar al-Sunna, which has carried out bombings in Iraq and an attack that killed 22 people in the dining hall of a US base at Mosul last Christmas.
Two others were Muhammad's Army and the Islamic Army in Iraq, which in August reportedly killed Italian journalist Enzo Baldoni, the newspaper said.
One of the Americans at the talks introduced himself as a Pentagon representative and declared himself ready to "find ways of stopping the bloodshed on both sides and to listen to demands and grievances", The Sunday Times reported.
The US officials tried to gather intelligence information about the structure, leadership and operations of the groups, which irritated some of their members, the report said.
The groups had been told that the talks would consider their main demand, a timetable for the withdrawal of US forces from Iraq, The Sunday Times said.
During the 13 June talks, the US officials demanded that two other anti-US groups - the 1920 Revolution and the Mujahidin Shura Council - cut any ties they have with the country's most-feared group, al-Qaida in Iraq.
Bombings have destabilised
Iraq since the US-led invasion
In television appearances on Sunday, Rumsfeld sought to downplay the importance of the meetings.
"My understanding is some London paper reported this and everyone is chasing it," he told the Fox News Channel.
"I would not make a big deal out of it. Meetings go on frequently with people."
Discussing the report on the ABC TV network, the defence secretary said: "I get reports on dozens of meetings. If you're asking: 'Are the Iraqis - whose country it is - reaching out to the Sunnis?' Yes, they are.
"Are our people involved in helping them? Sure," he added. "We talk to people all the time."
However, he did not say whether US officials had met Iraqi anti-US groups.
No one was immediately available for comment at the US embassy in London, and military officials in Baghdad did not immediately respond to a request for comment.
However, on 7 June, Iraq's former electricity minister, Ayham al-Samarie, said two groups - the Islamic Army in Iraq and the Army of Mujahidin - were willing to negotiate with the Iraqi government, possibly opening a new political front in the war-torn country.
Ansar al-Sunna has claimed
responsibility for anti-US attacks
Al-Samarie, a Sunni Muslim, said he had established contact with groups that were responsible for a large part of the violence in Iraq, including assassinations and kidnappings.
A senior Shia legislator, Hummam Hammoudi, also said recently the Iraqi government had opened indirect channels of communication with some anti-US groups.
The contacts are "becoming more promising and they give us reason to continue", Hammoudi said, without providing details.