However, Lt. Gen. Raymond Odierno also warned that he may not be able to make a full assessment of the situation in Iraq by September, as demanded by lawmakers.
And as American troops move into new parts of the country, they're suffering higher casualties as they run into deeply-buried, impossible to see explosive devices — the infamous IEDs, reports CBS News national security correspondent David Martin.
Odierno, the No. 2 U.S. commander in Iraq, told Pentagon reporters by videoconference that he is pressing his military officers to reach out to the tribes, to some small insurgent groups and to religious and political leaders to push them to stop the violence.
"We are 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," Odierno said from Camp Victory in Baghdad. "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."
Stemming the violence in and around the capital city is key to giving the Iraqi government time to stabilize and move toward reconciliation with the warring sectarian factions. That would then allow the United States to begin withdrawing troops.
U.S. military officers tell CBS News the troop surge, which has now reached full strength, stands no chance of succeeding by September.
That's the critical month Gen. David Petraeus, the American commander in Iraq, is scheduled to report to Congress, reports Martin. Petraeus wants to deliver the report before the Muslim holy month of Ramadan begins on Sept. 13.
That's because Ramadan usually brings a spike in violence that would make it harder for Plateaus to claim even modest progress, adds Martin.
Odierno said he believes that about 80 percent of the enemy fighters, including key Sunni insurgent groups and Shiite militia, could be brought into the political process. The remainder, he said, are largely al Qaeda operatives who will have to captured or killed.
He cautioned that the process will be slow. And he repeatedly warned that he may need more time to determine if the military buildup ordered by President Bush earlier this year has begun to work.
He said he will provide his report in September as required.
In other developments: