(Updates with news conference)

By Mussab Al-Khairalla

BAGHDAD, Dec 21 (Reuters) - New Australian Prime Minister Kevin Rudd made an unannounced visit to Iraq on Friday and pledged continued help in training Iraqi soldiers and police after 550 Australian troops are withdrawn next year.

Australia was one of the first countries to commit troops to the U.S.-led invasion of Iraq in 2003, but Rudd, who swept aside 11 years of conservative rule in a national election on Nov. 24, campaigned on a promise to bring frontline forces home.

Australian troops are based mainly in Dhi Qar province in Iraq's more peaceful Shi'ite Muslim south, where they help maintain security and train Iraqi forces. Australia has about 1,500 troops in and around Iraq.

After visiting the troops in Dhi Qar, Rudd held talks with Prime Minister Nuri al-Maliki in Baghdad to discuss improving economic cooperation and training Iraq's security forces, which have been rebuilt since the U.S.-led invasion in 2003.

"We have agreed to increase the trade volume through importing and exporting. We also agreed on the need for Australian companies to invest in Iraq, in the oil sector and others," Maliki told a news conference.

Rudd said there was a plan to train Iraqi police officers in third countries in the region and to offer Iraqi soldiers training in Australia.

Australia is keen to regain its role as a major wheat supplier to Iraq, one of the world's biggest importers. Iraq last year switched to buying most of its wheat from the United States.

Iraq agreed with Australia in October to resume wheat sales by mid-2008 after suspending dealings with the Australian Wheat Board (AWB) in February 2006 as an Australian judicial inquiry began probing allegations that the AWB had paid $222 million to Saddam Hussein's government in kickbacks. (Writing by Ross Colvin; reporting by Mussab Al-Khairalla; editing by Andrew Roche)

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