There has been fierce fighting in recent days as government forces have tried to force militants aligned to the Islamic State of Iraq and the Levant (ISIS) out of Ramadi and Fallujah.
An AFP news agency journalist told the BBC that black flags used by jihadists were still flying in both cities.
Clashes erupted on Monday after troops dismantled a protest camp in Ramadi.
Local Sunni Arabs had been demonstrating for months against what they perceive as discrimination by the Shia-led government and unfair targeting of their minority community by anti-terrorism measures implemented to stem the surge in sectarian violence.
But Prime Minister Nouri Maliki ordered that the sit-in be cleared, alleging it had "turned into a headquarters for the leadership of al-Qaeda".