New Defence Secretary John Hutton met British troops in Basra.
Mr Hutton also toured markets and chatted with locals in the southern Iraqi city.
Speaking after his visit, the minister said: "We want to focus on training and education to get us closer to our aim of passing full control to the Iraqi authorities.
"We are getting closer to achieving this goal and I hope we can reach the point when we can consider a significant change to our mission here next year.
"This massive progression is due to the efforts of every British service personnel and civilian who has served here, and I am hugely proud of what they have achieved."
Mr Hutton met members of the 2nd Battalion The Royal Anglian Regiment (The Poachers), who are currently acting as the military transition team and training Iraqi forces.
Over the weekend he visited Baghdad and hinted that most UK troops could be out of the country by early next year.
