"Because there are insurgents reaching out to us ... we want to reach back to them," Lieutenant General Raymond Odierno told reporters in a teleconference from Iraq.

"And we're talking about cease-fires and maybe signing some things that say they won't conduct operations against the government of Iraq or against coalition forces," he added.

"We have organised ourselves to be more aggressive in this area. We believe a large majority of groups within Iraq are reconcilable, and are now interested in engaging with us. But more importantly, they want to engage and become a part of the government of Iraq," he said.

Based on the US-Iraqi forces' "initial success" in increasing security in Anbar province, he added, "we now see opportunities for further engagement across Iraq with other tribes and entities, to include mainstream Sunni and Shia insurgents."

Odierno provided an update of the US troop "surge" announced in January as part of a new last-ditch effort to restore security to the country, focused on Baghdad and Anbar province.

He said that US and Iraqi troops have not yet made sufficient inroads in their campaign to quell the violence in Baghdad.

"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," he said.

He acknowledged that the violence had risen again in May compared to April, despite the ongoing US troop increase.