Ramadi is the provincial capital of Anbar, formerly a stronghold of Iraq's Sunni fighters.
Violence in the region has dropped from its peak in 2006 and 2007, but bombings and assassinations remain common.
On Friday, unidentified assailants killed Sheikh Abdulalim al-Saadi, the imam of a mosque in Ramadi and the brother of the mufti of Iraq.
Two police officers were killed by a roadside bomb in the province on Thursday.
Later that day, officers arrested four armed men wearing explosive belts. The men had a large cache of weapons, including four rockets and nearly three dozen bombs, according to local police.
A series of other attacks in the last two weeks have targeted police, a hospital, and several jewellery shops.
Many Iraqis worry that the ongoing political impasse, with no one able to form a government four months after parliamentary elections, will lead to increased violence.
Joseph Biden, the US vice-president, is in Iraq this week trying to encourage a resolution to the stalemate.