Defence Secretary John Reid is visiting British troops in Basra, as part of series of meetings in Iraq.
John Reid has denied Iraq is in the grip of a civil war
The visit coincides with the third anniversary of the coalition invasion.
While there he has said Iraq has seen "real progress", and has denied British troops do no want to serve because they disagree with the war.
As protesters marched in London Mr Reid called on them to instead support the UN and democracy in Iraq - comments the organisers branded "disgraceful".
The minister has told troops that those trying to provoke a civil war in Iraq were failing.
He was speaking after Iraq's former prime minister Iyad Allawi said he believed the country was in the grip of a civil war.
On Saturday, Iraqi President Jalal Talabani said he had briefed Mr Reid on current talks to form "a national unity government, which we consider to be the key for solving all problems in Iraq".
Ahead of the meeting in Baghdad Mr Reid had this should be Iraqi politicians' highest priority.
At a news conference after the meeting, Mr Talabani said discussions were held on the building of the Iraqi army and police forces, and the presence of British troops.
"Once we finalise building our forces we shall bid them farewell with respect. He [Mr Reid] expressed his government's willingness to stay until the Iraqi government asks them to leave."
Mr Reid's visit has also included meetings with Iraqi defence minister Saadoun al-Dulaimi and top US commander Gen George Casey.
The UK minister praised progress by Iraqi security forces but said they were not ready to control whole provinces.
The government announced last week that UK troop numbers are to fall by 800 to 7,000.