Lieutenant-General Raymond Odierno said that about 80 per cent of those fighting US forces were thought to be ready to join Iraq's political process.
He said: "We're talking about ceasefires and maybe signing some things that say they won't conduct operations against the government of Iraq or against coalition forces."
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US commanders hope to convince local Iraqi resistance groups to split from groups such as al-Qaeda in Iraq.

"We have organised ourselves to be more aggressive in this area," Odierno said.
"We believe a large majority of groups within Iraq are reconcilable, and are now interested in engaging with us."

In the western province of Anbar, tribal leaders have turned on al-Qaeda in Iraq.
And on Thursday, residents of west Baghdad reported that members of the 1920 Brigades group were fighting their former al-Qaeda allies. Al Jazeera said quoting Iraqi police sources that up to 12 armed men were killed in clashes between fighters from al-Qaeda in Iraq and Sunni fighters in Amiriya district.
The clashes caused damage to residential areas and forced many families to flee the neighbourhood.

'Tough month'

Brigadier-General Perry Wiggins, deputy director of regional operations with the US joint chiefs of staff, admitted on Wednesday that May had been "a tough month".

He said: "We're moving into places where we haven't been, not necessarily before."

Two US soldiers were killed by a roadside bomb on Wednesday in the southwest corner of the capital, a ward of battered neighbourhoods that has seen intense fighting. A separate explosion that day killed two others on foot patrol.
Another soldier was killed earlier this week by a roadside bomb northwest of the capital, and a US soldier died of "non-battle related causes," the military announced on Thursday.

April and May together were the deadliest two months since the war began.

Troop 'surge'
May's casualties coincide with a "surge" in US reinforcements, which is due to peak next month.
"We have not made the progress that I think is necessary yet, but I hope over the summer that we will continue to make progress"

Lieutenant-General Raymond Odierno
Under this plan, US and Iraqi troops are basing themselves in exposed patrol bases in order to control Baghdad street by street.
Odierno conceded that the Baghdad security crackdown has not yet made sufficient inroads.

He said: "We've made small progress here. We have not made the progress that I think is necessary yet, but I hope over the summer that we will continue to make progress.
"But it is still down from what it was when we started this surge operation in January in Baghdad. There are some positive signs.
"Civilian deaths are down in Baghdad. Sectarian deaths are down."

Falluja bombing

Odierno's remarks came against a backdrop of continued violence. On Thursdsay, in the central Iraqi city of Falluja at least 20 people were killed and another 20 wounded by a suicide bomber, a hospital source said.
A bomber wearing an explosives vest walked up to a queue of young men at a police recruitment centre and detonated the bomb, the source said.
Falluja, 50km west of Baghdad, is in Anbar province, a stronghold of Sunni armed groups.
Seven Iraqis, among them three policemen, were killed and 20 others injured when a booby-trapped truck blew up at a postal compound in Ramadi, Iraqi police sources said.
Elsewhere, dozens of civilians were killed or wounded after being fired upon by militias in northeast Baghdad's Khalis district, Al Jazeera reported quoting the mainly Sunni Association of Muslim Scholars (AMS).