But although he showed support for Nuri al-Maliki by flying in two days after a unity government of Shia, Sunnis and Kurds was sworn in, Tony Blair would not be drawn on deadlines.
Blair told a joint news conference with al-Maliki in Baghdad on Monday. "What we want to see in Iraq is a sovereign and independent nation ... with Iraqis in control of every aspect, including their security."
A senior official with Blair said Britain hoped all combat troops would leave during the new government's four-year term.
"The aim is to take Iraq to a position where the multinational force is able to withdraw during its period in office," he said, in the firmest such comment yet from one of the two main Western allies on Iraq.
More training needed
But al-Maliki said Iraqis needed more training and equipment and conceded that a profusion of forces posed a risk of civil war.
He did say, however, that two British-run southern provinces, Muthanna and Amara, could be handed to Iraqi security forces next month.
And a statement issued by the Iraqi and British governments said that "by the end of this year, responsibility for much of Iraq's territorial security should have been transferred to Iraqi control".
Only Baghdad and al-Anbar, where a US marine was killed on Sunday, would be left under US control by December, al-Maliki said.
Two bomb attacks killed nine people in Baghdad while Blair visited on Monday. At least 20 other violent deaths were reported around the country. Officials say dozens of people are killed daily.
"It's been longer and harder than any of us would have wanted it to be, but this is a new beginning," said Blair.