BAGHDAD (AFP) - Fighting in the Iraqi city of Ramadi, where the Islamic State in Iraq and Syria (ISIS) group is threatening to take full control, has displaced around 8,000 people in two days, the International Organisation for Migration said Sunday.

A renewed ISIS assault, which began late Thursday, saw extremist fighters seize the government compound in Ramadi, the capital of Anbar province.

"An estimated total of 1,296 families (7,776 individuals) have been displaced, and numbers are increasing," the IOM said.

The displaced families went to Amriyat al-Fallujah, to the east, but have not been allowed to cross the Euphrates and enter Baghdad province.

Thousands of civilians had already fled the city during previous waves of violence, including an offensive last month.

According to the IOM, the number of people displaced by Iraq's conflict since the beginning of 2014 has reached a new high of more than 2.8 million.

Using waves of suicide car bombs, ISIS took over several central Ramadi neighbourhoods on Friday, leaving the last government forces in the city confined to a handful of positions.

According to police sources, fighting took place Sunday in the Malaab neighbourhood in eastern Ramadi, one of the last districts where government forces were still present.

Hundreds of forces were hunkering down in their bases in northern parts of Ramadi, waiting for reinforcements promised by Prime Minister Haider al-Abadi.

Taking full control of Ramadi, about 100km west of Baghdad, would be the most significant victory this year for ISIS, which has suffered a string of setbacks elsewhere in the country.