Mr Blair was more vague than the Iraqi prime minister. He insisted that there was no timetable and that the handover to Iraqi forces would depend on the prevailing conditions.
Both Mr Maliki and Mr Blair's comments were telling. With the arrival at last of an Iraqi government, the US and British can at last begin to plan for specific withdrawals. The planes to carry troops home can be booked.
The US has 133,000 servicemen and women in Iraq and the British 8,000. The combined Iraqi army and police have 263,000 at present and are predicted to have a strength of 320,00 by the end of the year. British and US troops withdrawals are scheduled to begin this summer and by the end of the year there will have been significant reductions, even though there will still be a sizeable presence for anything between four and 10 years.
Mr Maliki said by the end of the year Iraqi forces could have taken control of all the provinces except Anbar, to the west of Baghdad and where the insurgency is strongest, and Baghdad itself.
The British forces have responsibility for four provinces: Muthanna, Maysan, Basra and Dhi Qar (where Italian troops are stationed). Muthanna, which is to the west of Basra and contains relatively small towns such as Samawa that sit beside the Euphrates, will be the first to be handed over. Compared with the rest of Iraq, Muthanna has been relatively quiet. British forces would expect to have completed their withdrawal within a matter of weeks of the July handover.
Next up will be Maysan, to the north of Basra and where British forces have suffered heavy losses. But the violence has tended not to be from organised insurgency but from criminal gangs in what is one of the poorest parts of Iraq, and from renegade bands who were active even under Saddam Hussein.
As part of the agreement, the Iraq army and police have to demonstrate they are competent to deal with various problems. There is a long tick-list they have to satisfy, not only their ability to fight insurgents but to demonstrate that the police, as well as the army, is relatively sectarian-free.
The remaining two provinces in British hands will prove more difficult to hand over, in part because Basra is becoming more unruly and in part because the police force there is riven with sectarianism. The British hope is that they will have withdrawn 3,000 personnel from Iraq by the end of the year.
The US withdrawal is more problematic, mainly because the Americans are facing a more sustained insurgency campaign. But the intensity of the fighting in Baghdad, Anbar and, until the middle of last year, Nineva overshadows the relative peace in other parts of the US sector. First up for withdrawal is expected to be Najaf, the holy Shia city.
The US had been planning for the Iraqi forces to take over by July half of what the Pentagon refers to as its "battlespace". But that was before the insurgents increased their attacks in the past few months, killing hundreds of Iraqi civilians. Insurgent attacks on US forces in March and April were at their highest since last autumn.
US and British officers have said that the next few months are crucial as insurgents try to undermine the new government. For this reason, some US officers have been recommending to the Bush administration that it is the wrong time to be handing over to Iraqi forces. Other voices in the US army have been warning that there is a huge gap between the Iraqi forces on paper and their actual ability.
In a report to the Pentagon, General Barry McCaffrey, a retired army commander who teaches international affairs at West Point, said the Iraqi army was badly equipped, with only a few light vehicles and almost no mortars, heavy machine guns, decent communications equipment, artillery, air cargo transport, helicopter troop carriers or strike aircraft of its own.
