BAGHDAD, Jan 5 (Reuters) - Iraqi Prime Minister Nuri al-Maliki returned to Baghdad on Saturday and said he was in good health after flying to London a week ago for medical tests.

"We're back to continue the process of reconstruction hand in hand with all brothers ... working in this very sensitive phase in the history of Iraq," he told reporters at Baghdad airport.

"I'm assuring my brothers my health is very good and I will resume office immediately," he said.

Maliki flew to London on Dec. 29 for unspecified tests and met British Prime Minister Gordon Brown for talks while he was there. An official in Maliki's office said the Iraqi prime minister had been suffering from mild exhaustion.

Maliki will be under pressure from Washington in the coming year to build on military gains that have improved security by passing key laws seen as crucial to promoting national reconciliation between Iraq's Shi'ite and Sunni Muslims.

The main political blocs have so far failed to agree a new law that will equitably share Iraq's oil wealth and measures to allow provincial elections to be held in 2008 and former members of Saddam Hussein's Baath party to return to public life. (Reporting by Ahmed Rasheed, Writing by Ross Colvin; editing by Sami Aboudi)

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