It is partly a "getting to know you" visit for the new defence secretary
Britain and Iraq have agreed to begin immediate negotiations on the future role of UK forces.
New Defence Secretary John Hutton, who is on a surprise visit to Baghdad, said talks would start soon on a new mandate based on a similar pending US deal.
That agreement, hammered out over many months, has run into trouble in winning political Iraqi approval.
Mr Hutton also said the process of reducing troop numbers from the current 4,100 could begin early next year.
The MP, who took over the defence job just over two weeks ago, said he wanted to reach a deal with Iraqi Prime Minister Nouri al-Maliki on the future of UK troops before the current UN Security Council mandate ended on 31 December.
"I have just come from a meeting with the prime minister and we're going to intensify those discussions, and he and I both agreed that we should get this agreement reached as soon as possible - and certainly well before the expiration of the UN mandate," he told the BBC.
John Hutton on the role of UK forces after the UN mandate expires
A long-term security pact between Iraq and the US, on which the British want to base their own bi-lateral deal, has faltered after Iraq's ruling coalition said it wanted to make changes to the draft outline.
The pact would allow US forces to stay in Iraq until 2011 and permit Iraq limited authority to prosecute troops.
If nothing is agreed by the end of the year, Iraq will have to go back to the UN to ask for a renewal of its mandate to cover the activities of all coalition forces.
After talks with Mr al-Maliki and Iraq's Defence Minister General Abdul Qadir, Mr Hutton said the 4,100 British service personnel currently in Iraq would be reduced from the beginning of next year as they take on a role providing training and education for the Iraqi forces.
"We want, in the first months of next year, to see a fundamental change in our military mission in Iraq, moving towards an increased focus on military training and education as part of a broad-based bilateral partnership," he said.
We want, in the first months of next year, to see a fundamental change in our military mission in Iraq
Mr Hutton, on his first trip to Iraq, also met the small number of troops still operating in Baghdad, visiting members of the 2nd Battalion The Royal Anglian Regiment and others based in the Baghdad Support Unit.
Their principle role is to provide escorts and protection for resident and visiting British officials and military officers.
Mr Hutton said he wanted to see what British civilians and military were achieving and "get a clear sense of the UK's engagement with Iraq, both current and future".
"Throughout the country security and prospects are improving and I am extremely proud of what our forces have achieved - they continue to do a tremendous job," he said.
"I pay tribute to Prime Minister Maliki and the government of Iraq for their leadership and to the Iraqi security forces for their hard work and sacrifice in achieving this."
Mr al-Maliki said earlier this month that British combat troops were no longer needed to maintain security in southern Iraq.
Although he said he wanted some to stay on and continue training Iraqi security forces and the navy, exact numbers and the timetable for a reduction in UK troop levels have yet to be negotiated.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.