Tony Blair told a joint news conference in the fortified Green Zone on Monday: "It's been longer and harder than any of us would have wanted it to be but this is a new beginning."
He highlighted the involvement of all Iraq's groups in the new national unity government sworn in on Saturday.
Nuri al-Maliki, the Iraqi prime minister, said he was keen to press on with Iraqi forces taking over security from US and British troops but said they would need more training.
Earlier, a British official said foreign troops could be effectively out of Iraq in four years, the clearest indication of a timetable yet from the two main allies who invaded to topple Saddam Hussein three years ago.
Blair said the establishment of a unity government means that there is no longer any justification for armed uprising and that the best way to get foreign soldiers to leave is for fighters to lay down their arms.
"The important thing is that for the first time we have a government of national unity that crosses all boundaries and divides, that is there for a four-year term and that it's directly elected by the votes of millions of Iraqi people," Blair said.
"There is now no vestige of excuse for anyone to carry on with terrorism or bloodshed.
"If the worry of people is that they may be excluded from the political process, we now have Sunnis, Shias and Kurds in the leadership.
Blair declined to comment on a
timetable for UK troop pullout
"If the worry of people is the presence of the multinational forces, it is the violence that keeps us here. It is the peace that allows us to go."
Blair said Britain will work with al-Maliki "to make the hopes and expectations of the Iraqi people for the future a reality".
Al-Maliki said Iraq now was better off than it was under Saddam's government, despite the rampant violence. He said Iraqis had produced a "full democratic regime and defeated the enemies of democracy".
He also said US-led forces will hand over security responsibility to Iraqi forces in two provinces from next month.
Civil war fear
Al-Maliki said Iraq could face civil war if militias are not disbanded. "Weapons should be in the hands of the government and no militias should be outside the control of the government," he said.
"Otherwise this will lead to ... a civil war."
"There's an agreement and, according to this schedule for handing over security, Samawa and Amara provinces will be handed over to Iraqis in June and by the end of this year this operation will be completed except for Baghdad and maybe Anbar."
Blair declined to be drawn on a timetable for withdrawal.
"Weapons should be in the hands of the government and no militias should be outside the control of the government"
Iraqi prime minister
Al-Maliki's timetable, which would coincide with the expiry of a UN mandate for the US-led multinational force, is more ambitious than anything voiced publicly by US or British commanders, who stress that any withdrawal will depend on Iraqi forces being capable of ensuring security.
Samawa and Amara are southern, Shia provinces, largely peaceful and controlled by British troops. Their commanders have said they may withdraw from some provinces soon. Anbar is the western desert stronghold of Sunni Arab fighters.
Meanwhile, violence continued unabated. Car bombs and drive-by shootings left 16 people dead around the country on Monday, including seven police officers, security officials said.
A roadside bomb killed four police officers after exploding next to a patrol in Musayyib, about 60km south of Baghdad, police Colonel Ahmed Mijwel said.
In Baghdad, a car bomb exploded between a clinic and a market to kill three people and injure another nine in the Shia Amin neighbourhood, killing three civilians and injuring another nine, 1st Lieutenant Haider Hamil said.
Another bomb, this time in a car, killed two police officers and injured four people when it detonated next to a patrol in southeastern Baghdad's Zafaraniya neighbourhood, police Captain Ali Mahdi.
Al-Maliki: No militias should be
outside government control
Another roadside bomb missed a police patrol in eastern Baghdad Baladiyat's neighbourhood, injuring two civilians, police Lieutenant Ali Mitaab said.
Officials said assailants killed a police colonel and injured another officer in Samarra, north of Baghdad, an employee of a mobile phone company in Baquba, and the general director of the youth ministry in Baghdad.
The body of a police captain who was shot in the head, was found in the Aziziya area, south of Baghdad, officials said.