Tony Blair says it is "entirely reasonable" to talk about the possibility of British troops starting to leave Iraq next year.
Mr Reid said British withdrawal from Iraq will go in stages
But he said UK soldiers would not pull out until the job is done and Iraqi security services could take over.
He made the comments after talks with Iraq's vice president Abel Abdul Mahdi.
Iraq's president Jalal Talabani says an immediate withdrawal of multinational forces would be a "catastrophe" for Iraq and would lead to civil war.
Mr Blair said: "It is entirely reasonable to talk about the possibility of withdrawal of troops next year, but it's got to be conditioned by the fact that we withdraw when the job is done.
"And the job is, when the Iraqi security services are capable of dealing with the security problems they have, now the Iraqi capability is growing the whole time."
Mr Blair said that if the political process worked as well as was hoped, particularly after December's elections in Iraq, it would reinforce security in the country.
Defence Secretary John Reid said the whole process of troop withdrawal "could start within the next 12 months".
"We are not saying there would be immediate withdrawal. We are not saying that there is a immutable timetable, irrespective of conditions on the ground," he told BBC Radio 4's Today programme.
"We are not saying that everyone will be out by the end of 2006.
"We are saying that this process, despite the terrorist attempts to destroy it, is going relatively well, and, in the course of the next year, we could well see the handover to Iraqi forces at certain places in Iraq, including in our own area."
He said the British government did not have any "imperialist ambitions to stay" in Iraq.
Terrorists' attempts to destroy the country's fledgling democracy would only "delay our departure", he said.
In an interview on ITV1's Jonathan Dimbleby programme, President Talabani said Iraqis did not want foreign troops to remain indefinitely.
"Within one year....Iraqi troops will be ready to replace British forces in the south," he said.
He understood the British people were eager for their troops to return home.
"British people have full right to ask this, their sons coming back home, especially if they finished their main job, which was the ending of dictatorship," he said.
He called for a gradual pull-out, with close co-ordination between coalition nations and the Iraqi authorities.
General Sir Mike Jackson, the head of the British Army, said Mr Talabani's prediction of a British departure by the end of 2006 was "well within the range of what is realistically possible", but "it's a question of achieving the right conditions".
He told BBC1's Sunday AM programme: "We need to be careful about timetables and end dates. It is much talked about, but it is not the best way of looking at this."
Gen Jackson said he was "quite encouraged" by a visit last month to Iraq.
While accepting that the security situation was "rather less than anyone would wish", he stressed that incidents were largely confined to four of Iraq's 18 provinces.
The Liberal Democrats' defence spokesman, Michael Moore, said Mr Talabani's comments should "focus attention on the need for a clearly stated exit strategy from Iraq".
"The coalition must internationalise the support for the Iraqi authorities as part of a strategy which sets out the appropriate milestones for security, public services and the full transfer of sovereignty to the Iraqi people," he said.