He said he expected the roughly 133,000 US troops to be cut to less than 100,000 by year's end and an "overwhelming majority" of them to have left by the end of 2007 under a US-Iraqi plan for progressively handing over security.
"We have a roadmap, a condition-based agreement where, by the end of this year, the number of coalition forces will probably be less than 100,000," he told Reuters in an interview.
"By the end of next year the overwhelming majority of coalition forces would have left the country and probably by the middle of 2008 there will be no foreign soldiers in the country."
Iraqi and US forces said they had killed a leader of al-Qaeda in Iraq -- the group Washington says drives the bloodshed -- and Iraqi police and troops fought off raids by dozens of insurgents in Baquba yesterday which killed 30 people.
Humadi al-Takhi, a well-known figure locally and reputed to be a regional al-Qaeda chief, was killed in a raid on a house just outside Samarra, 100km north of Baghdad.
He is the third brother from his family to die as a senior member of al-Qaeda, and assumed the Samarra leadership last year when his elder brother Najim was arrested and later found dead.
Another al-Qaeda leader was arrested nearby yesterday.
Baquba, 65km north of the capital, was under curfew a day after at least 100 rebels attacked police and army posts with mortars, rockets and small arms fire.
Insurgents have been launching more and more bold operations against Iraqi soldiers and police, trying to handicap the security forces' abilities and strength.
Rubaie, an official of the outgoing government, was speaking after US Defence Secretary Donald Rumsfeld and Secretary of State Condoleezza Rice visited Baghdad to show America's support for Prime Minister-designate Nuri al-Maliki.
Maliki, a tough-talking Shi'ite Islamist, is forming a government of national unity Washington hopes will foster stability and allow it to begin withdrawing troops.
US President George W Bush has refused to set a timetable for a withdrawal, saying American soldiers will stand down as Iraq's take more responsibilities fighting Sunni rebels and tackling sectarian violence that has stoked fears of civil war.
While some US politicians have called for a timetable, administration officials say publicising a schedule for withdrawal would encourage their enemies.
The US commander in Iraq, General George Casey, told a news conference alongside Rumsfeld on Wednesday he remained on track to recommend cutting US troop levels this year.
Last year, Casey forecast a "fairly substantial reduction" in the US force this spring and summer but recently said the rise in sectarian violence would affect his decision. Although it is unclear if Rubaie will remain under Maliki, he said the "roadmap" was an "agreement between the Iraqi security forces, the Iraqi government and the (US-led) coalition".
"We are quite eager to assume security responsibilities," he said in his office in the heavily guarded Green Zone, adding Iraqi forces already played a "lead role" in 60 per cent of military operations and held 50 per cent of the "battle space".
Rubaie said he expected the new government, Iraq's first full-term administration since Saddam Hussein was toppled, will hold talks with the United States about the future status of US forces in Iraq and the military relationship between them.
Saddam, on trial on charges of crimes against humanity over the death of 148 Shi'ite villagers, turned 69 today. The occasion, once a major holiday, went largely unmarked.