Abu Abdel-Rahman al-Baghdadi, a key leader of the al-Qaeda linked Islamic State in Iraq and the Levant, was killed in clashes in the city of Ramadi, according to the report.
The Iraqi government has launched a military operation in Anbar against insurgents who last week took control of the cities of Fallujah and Ramadi.
Militants from the Islamist State in Iraq and the Levant have seized large areas in both cities after government forces cleared out an anti-government protest camp in Ramadi on Monday.
Police said Friday they had regained control of posts in Fallujah that had fallen to insurgents.
Anbar's police chief, General Hadi Razij told Alsumaria News that government forces had regained full control of Ramadi and were preparing to launch a security sweep across Anbar.
"We have coordinated with tribesmen and (pro-government) Sahwa fighters for a decisive battle with the armed groups," Razij said.
In December, the Iraqi military launched an operation in Anbar after 16 military personnel, including a senior commander, were killed in an attack by extremists with suspected ties to al-Qaeda.
NJF/NJF