Defence Secretary John Reid has denied UK troops do not want to serve in Iraq because they disagree with the war.
Mr Reid said the reduction was not part of a 'handover of responsibility'
There was no evidence of the forces struggling to find recruits, he added.
Visiting Iraq three years after the coalition invasion, Mr Reid met Iraqi defence minister Saadoun al-Dulaimi and top US commander Gen George Casey.
He told BBC Radio 4's PM programme he saw real progress, with thousands of schools and hospitals re-opening and Iraqis having access to consumer goods.
"It is just not true to say everyone is in despair and nothing is getting better," he added.
Mr Reid told PM: "To the best of my knowledge out of the 80,000 troops who have come through Iraq, there have been two cases of people saying they did not want to come back and resigning from the Armed Forces.
"I do not think that is atypical of any theatre of war."
Mr Reid praised progress by Iraqi security forces but said they were not ready to control whole provinces.
The government has announced UK troop numbers are to fall by 800 to 7,000.
The reduction comes as Iraqi security forces begin to take on more responsibilities for themselves.
US forces are currently carrying out a major operation targeting suspected Iraqi insurgents near Samarra, north of Baghdad.
In Baghdad on Friday, Mr Reid said: "We are not at the stage yet where the Iraqis feel happy and able to take over whole provinces, that will only be done by agreement with the Iraqi government and the multinational partners.
"When those conditions are met, we will be only too pleased to hand over to our Iraqi colleagues."
He added: "All coalition troops deserve to be thanked for their contribution, which includes real progress made in building up the Iraqi security forces.
"I have been very impressed by the professionalism and restraint shown by the Iraqi security forces in their handling of recent terrorist activities.
"The improving operational effectiveness of the Iraqi security forces will help to give Iraq what the vast majority of the Iraqi people want - a stable and secure future for their country."
The UK troops reduction means a total of 3,000 troops will have been withdrawn since October 2003, when there were 10,000 in Iraq.
Mr Reid said at the time of the announcement that there were now 235,000 members of the Iraqi security forces equipped and trained, with 5,000 more signing up every month.
And the Iraqi Army has 110 operational combat battalions carrying out counter-insurgency operations.
The reduction reflected the "completion of some of our security sector reform tasks to develop the capability of the Iraqi forces", he said, and improvements in the way UK forces were configured.
Mr Reid added that, despite continued violence in Iraq, civil war was "neither imminent nor inevitable".
"There is more sectarian tension and that is of course because the terrorists are trying to provoke that," he told PM.
But the minister added: "Despite the ferocity of the terrorist, the Iraqi people will not be defeated - and our will to see the job done will not be broken.
"Britain will not 'cut and run'.
"We will stay until the job is done, which means as long as we are needed by the Iraqi people and are wanted by the Iraqi government."
The US military has claimed that it is mounting near Samarra, north of Baghdad, its biggest airborne operation since the invasion.
The operation, targeting suspected insurgents and foreign fighters, is said to involve 50 aircraft and 1,500 troops.
But correspondents have suggested that the operation may not be as large as has been implied.