BAGHDAD (AFP) - Fighters from the Islamic State in Iraq and Syria (ISIS) closed in on the last government-held positions in the Iraqi city of Ramadi on Saturday after Baghdad vowed an air and ground counter-offensive.

After seizing the Anbar provincial headquarters on Friday, the militant group said it unleashed another fleet of suicide car bombs on key positions in Ramadi.

"Three suicide attackers in armoured vehicles tried to break into the 8th Brigade base. The attack was repelled using armour-piercing rockets," said Ramadi Mayor Dalaf al-Kubaysi, one of the last officials still in the city.

He said five soldiers were wounded.

Most of the Iraqi government forces and Sunni tribesmen fighting alongside them are concentrated in that base and in the Anbar Operations Command across the Euphrates river.

Civilians fled en masse as the militants took over several central neighbourhoods on Thursday and Friday and looked on the brink of claiming full control of the city.

The loss of the capital of Anbar province, which Prime Minister Haider al-Abadi had said would be the next target of government forces after wresting back Tikrit last month, would be a major setback.

After meeting top security officials in Baghdad on Friday, Abadi vowed his government would not abandon Ramadi.

The army sent reinforcements from Baghdad and elsewhere in Anbar, with local officials saying Iraqi and US-led coalition aircraft were also in action, but there was little sign of a major counter-offensive inside the city on Saturday.

"Security forces in Ramadi are taking position against the attacks of Daesh, mainly in the areas of Malaab and Operations Command," Kubaysi said, using an Arab acronym for ISIS.

"There are no military operations to take back the areas that were captured by Daesh," he said.

Jessica Lewis, research director at the Institute for the Study of War, said the government could not afford to let Ramadi fall completely.

"The Iraqi security forces will not let Ramadi go to ISIS without a massive fight," she said.

"It is key terrain. Not only is it Anbar's capital city, but it is also a military gap in ISIS's control line in Anbar," Lweis said.

Ramadi lies about 100 km west of Baghdad. ISIS holds Fallujah, about halfway between the two, and several key towns in western Anbar between Ramadi and the Syrian border.