Iraqi security forces and allied tribesmen have retaken areas in the central cities of Ramadi and Fallujah from Islamist insurgents.
A correspondent in Ramadi for RFE/RL said police forces and their Sunni tribesmen allies had taken back police stations in several neighborhoods in the city that had been ransacked and occupied by militants.
But he said some parts of Ramadi, the capital of Anbar Province, were still controlled by the insurgents, and fighting was continuing.
He said security forces made less progress against insurgents in nearby Fallujah, where neighborhoods near the highway to Baghdad are controlled by the Al-Qaeda-linked rebels.
Many insurgents took part in Friday Prayers along Fallujah's main street, some carrying black Al-Qaeda flags.
There was no clear count of killed and injured from the latest clashes, but some reports spoke of dozens of casualties.
The militants are trying to defend police stations and government buildings they seized on January 1-2, after army forces withdrew.
Washington has condemned "in the absolute strongest terms" the violence in Anbar Province.
" But let's be clear who is responsible for the violence; it's the terrorists who are behind it. That's why we're partnering with the Iraqi government, very closely, to fight this shared threat because at the end of the day, we can certainly helped them fight it, but we also want to help them build their own capability to do so themselves because ultimately that's the best way forward for Iraq," U.S. State Department spokesperson Marie Harf told reporters in Washington on January 3.
The Shi'ite-led government ordered the army to pull out of Ramadi and Fallujah this week, after Sunni tribesmen said they were ready to join police in the battle against Al-Qaeda militants.
Friday Prayers were held at Ramadi's Grand Mosque, where Mufti Adnan Mishawy urged worshippers to support government forces.
Fighting between Iraqi security forces and the Al-Qaeda-linked Islamic State in Iraq and Levant broke out on December 30 when a Sunni protest camp in Ramadi was dismantled by government forces.
Prime Minister Nuri Al-Maliki had vowed to shut down the camp, which had been set up more than one year ago. He said it had gone from a place of peaceful protest to a headquarters for Al-Qaeda forces.
With reporting by dpa and AFP