His inspection tour came as militants killed 22 soldiers and police over two days and kept their grip on part of the northern town of Sulaiman Bek in a new front in the persistent rebellion against his Shiite-led government in Sunni Arab areas.
The visit is Maliki's first announced trip to Anbar province since jihadist militants and anti-government tribesmen seized control of parts of Ramadi and all of Fallujah to its east at the start of the year, in a major setback for his government.
"We came to confirm our support to our people and our tribes in Anbar," Mussawi quoted Maliki as saying in a speech.
Another official in Maliki's office said the premier would be briefed on the progress of military operations.
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The prospects of a quick resolution to the crisis seem slim, with Deputy Prime Minister Hussein al-Shahristani saying the strategy for retaking Fallujah is to surround it and wait for Sunni Arab gunmen to run short of weapons and equipment.
Local official Talib al-Bayati told AFP security forces had succeeded in retaking militant-held areas yesterday, but then withdrew for unknown reasons.
Today, gunmen were in control of the town's Al-Askari neighbourhood, he said.