Iraqi government forces pressed their assault on militant strongholds in Anbar province Sunday as attacks elsewhere in the country killed seven people, with intensifying violence fuelling fears of a return to all-out conflict.

The effort to win back parts of Ramadi, capital of the western province of Anbar and one of two cities that either entirely or partially fell out of government control weeks ago, comes with violence at its highest level since 2008.

Soldiers and police fought alongside armed pro-government tribesmen in southern Ramadi in some of the heaviest clashes of recent weeks, a police officer and an AFP journalist said.

Acting defence minister Saadun al-Dulaimi was visiting the city as government forces made slow progress in their efforts to retake some militant-held neighbourhoods.

The renewed government assault came a day after the defence ministry announced warplanes and artillery had hit a neighbourhood in northern Fallujah, a rare military operation inside the city itself.

The army has largely stayed out of Fallujah, a short drive from Baghdad, fearing major incursions could ignite a protracted conflict with massive civilian casualties and damage to property.

US battles in the city, a bastion of militants following the 2003 US-led invasion, were among their bloodiest since the Vietnam War.

For weeks, anti-government forces have held parts of Ramadi and all of Fallujah, the first time they have exercised such open control in cities since the peak of violence that followed the invasion nearly 11 years ago.

The Al-Qaeda-linked Islamic State of Iraq and the Levant has been involved in the fighting, as have other militant groups and anti-government elements, while the police and army have recruited their own tribal allies.

The stand-off has prompted more than 140,000 people to flee their homes, the UN refugee agency said, describing it as the worst displacement in Iraq since the peak of the 2006-2008 sectarian conflict.

Elsewhere in Iraq on Sunday, attacks in and around Baghdad and the northern cities of Kirkuk and Mosul killed seven people, security and medical officials said.

Violence has spiked markedly in recent months, with more than 1,000 people killed across the country in January, the highest toll for a month since April 2008, according to government data.