The militants have captured several areas west of the city since the fighting broke out yesterday afternoon, while also seizing one police station and blowing up a second.
The fall of Ramadi, a city west of Baghdad where anti-government fighters have held shifting areas since the beginning of the year, would be a major advance for the militants who have overrun large areas of five provinces, including further reaches of Anbar.
Anti-government fighters subsequently seized parts of Ramadi and all of Fallujah, the first time they had exercised such open control in major cities in years.
Jihadist-led militants then launched a major offensive last month, bearing down on the capital from the north and west, but have so far been held off by security forces backed by Shiite militias and civilian volunteers.