Britain intends "to hold its nerve" in Iraq, Prime Minister Tony Blair has told Iraq's deputy prime minister.
Mr Blair discussed the present security situation in Iraq
No 10 denied that Mr Blair had pressed Barham Salih, during talks in London, for assurances his forces could take over policing south Iraq within a year.
Foreign Secretary Margaret Beckett said there would be no "rash" deadlines, adding that the UK would only leave once the Iraqi government could "cope".
The talks came as the Lib Dems called for a Commons debate on pulling out.
Sir Menzies Campbell, leader of the UK's third largest party, which opposed the war, said: "Surely Parliament should now be allowed to debate whether we stay or go."
Earlier on Monday, after meeting Mr Blair in Downing Street, Mr Salih said the UK and US could not "cut and run... and leave the Iraqis to face these difficult challenges on our own".
But he added: "We understand this is not an open-ended commitment by the international community."
Iraqi forces would assume control of the country province by province, he added.
Later, before meeting Mr Salih, Mrs Beckett, told BBC Radio 4's World At One said: "It would be a mistake to set some kind of false deadline. This is going step by step as it is possible and practicable to move forward."
Asked what sort of Iraq she envisioned being left behind, she said one that was democratic, which could "cope" and that was "back on its feet".
She said it was always "over-optimistic" to expect to create within three years a democracy like Britain's which had taken hundreds of years to develop.
Asked her views on whether or not Iraq might fragment, she said: "Everyone has been very keen to keep everyone together but in the longer term... it is not for us to say 'you will do this or you will do that'."
Pressed on whether it would be a disaster if Iraq split up, Mrs Beckett replied: "If that is what they want and they feel it is workable that is another matter."
The meeting between Mr Blair and Mr Salih came as the Iraqi government said it had imposed a curfew in the southern town of Amara after battles between Shia militias and police in recent days.
Amara, in Iraq's south, has been blighted by recent violence
At the weekend US President George W Bush said military tactics in Iraq would keep changing to deal with insurgents, but the US would not abandon the goal of building a strong democracy.
The issue of Iraq, and possible changes in strategy have been increasingly high profile in the US ahead of the elections next month for Congress.
Meanwhile a US state department official who said that his country had shown "arrogance and stupidity" in Iraq has apologised for his comments.
Alberto Fernandez, who made the remarks to Arabic TV station al-Jazeera, said he had "seriously misspoken".
In the UK, shadow foreign secretary William Hague asked the government to give MPs a "frank" assessment of the changing situation.
He said a review going on in Washington should be mirrored by a "careful reassessment" in London.
Defence Secretary Des Browne and Foreign Office Minister Kim Howells have both suggested recently that local forces should be able to take over within a year or so.
Britain has about 7,000 troops stationed in southern Iraq around the second city of Basra.
Last week the head of the Army, General Sir Richard Dannatt, was quoted in the Daily Mail as saying British troops "exacerbated" Iraq's security problems and should withdraw "some time soon".
Major General Richard Shirreff, in charge of UK forces around Basra, told BBC Radio 4's Today programme that forces were beginning to "get on the front foot".
He added: "There are signs we are beginning to see a tipping point where success breeds success.
"We are not there yet. We are beginning to win hearts and minds."