Iraqi forces advanced on three fronts against the Takfiri group, ISIL, flushing out pockets of resistance in and around Baiji and closing in on Ramadi and Hawijah.

Iraqi forces advanced on three fronts against the Takfiri group, ISIL (so-called Islamic State in Iraq and Levant) on Sunday, flushing out pockets of resistance in and around Baiji and closing in on Ramadi and Hawijah, officers said.

Iraqi security and allied paramilitary forces last week launched a broad offensive on Baiji, about 200 kilometers north of Baghdad.

The city and nearby refinery -- the country's largest -- have been one of the worst flashpoints since ISIL launched a sweeping offensive across Iraq's Sunni Arab heartland in June 2014.

Anti-ISIL forces, including thousands from the Popular Mobilisation (Hashed al-Shaabi) force have reconquered most of Baiji and its surroundings.

"They are still combing some neighborhoods of Baiji, including Tamim to the west and the market area in the center," a police brigadier general said.

"There are still a few IS members in there," he said.

"The security forces and Hashed forces took up positions to take control of some neighborhoods in Baiji, searching for bombs and booby-trapped houses," an army major general said.

He described the latest advance in the Baiji area as "the biggest victory since 10th of June 2014", when IS made massive territorial gains with a lightning offensive that saw Iraq's federal forces collapse completely.

Since they launched a counter-attack last year, government and allied forces have retaken all areas south of Baghdad and others north of the capital, including the city of Tikrit.

The government forces pushed past Baiji on the main road leading north to Mosul, cutting off ISIL insurgents holding the city of Hawijah, east of the Tigris river.

Army and police, backed by hundreds of Sunni tribal fighters incorporated into the Hashed al-Shaabi, began an operation Sunday aimed at surrounding Hawijah.

"The operation started in two areas, one west of Kirkuk around Al-Fatha and the other south of Kirkuk near Allas oil field," a major general said.

The Kurdish peshmerga forces were not directly involved in this operation but they have made progress of their own in recent weeks, pushing southwest from Kirkuk, which they control.