Iraqi security forces and militias fought their way into Saddam Hussein's home city of Tikrit on Wednesday, advancing on two fronts in their biggest counter-offensive so far against Islamic State militants.

In a possible response to the fighting north of Baghdad, militants in the Islamic State stronghold of Anbar west of the capital launched 13 suicide car bomb attacks on army and security positions in the provincial capital of Ramadi.

Army and militia fighters captured part of Tikrit's northern Qadisiya district, the provincial governor said, while in the south of the Tigris river city a security officer said another force made a rapid push towards the centre.

"The forces entered Tikrit general hospital," an official at the main military operation command centre said. "There is heavy fighting going on near the presidential palaces, next to the hospital complex."

Islamic State fighters stormed into Tikrit last June during a lightning offensive that was halted just outside Baghdad. They have since used the complex of palaces built in Tikrit under Saddam, the executed former president, as their headquarters.

More than 20,000 troops and Iranian-backed Shi'ite Muslim militias known as Hashid Shaabi, supported by local Sunni Muslim tribes, launched the offensive for Tikrit 10 days ago, advancing from the east and along the banks of the Tigris.

On Tuesday they took the town of al-Alam on the northern edge of Tikrit, paving the way for an attack on the city itself.

"The governor of Salahuddin announces the purging of half of Qadisiya district, the largest of Tikrit's neighbourhoods," a statement from governor Raed al-Jubouri's office said.

The army and militia fighters raised the national flag above a military hospital in the section of Qadisiya they had retaken from the militants, security officials said.

After pausing while helicopters attacked Islamic State snipers and positions, the ground forces were progressing steadily, taking "one street every 30 minutes", the security official said. He said there was fierce fighting around Tikrit police headquarters just south of Qadisiya.

To the northwest, troops and Hashid Shaabi fighters clashed with Islamic State militants in the industrial zone, he added.

Another official said later on Wednesday that six soldiers and militia fighters were killed by sniper fire in Qadisiya in the evening. He said the advance had been halted by a combination of sniper fire and heavy fighting, and the attacking forces were waiting for militia reinforcements.

RAMADI ATTACKS

If Iraq's Shi'ite-led government retakes Tikrit it would be the first city clawed back from the Sunni insurgents and would give it momentum in the next, pivotal stage of the campaign -- recapturing Mosul, the largest city in the north.

Mosul is also the biggest city held by the ultra-radical Islamic State, who now rule a self-declared cross-border caliphate in Sunni regions of Syria and Iraq.

Over the past few months Islamic State has gradually lost ground in Iraq to the army, Shi'ite militias and Kurdish peshmerga forces, backed by air strikes carried out by a US-led coalition of mainly Western and allied Arab states.

The United States says Baghdad did not seek aerial backup from the coalition in the Tikrit campaign. Instead, support on the ground has come from neighbouring Iran, Washington's long-time rival in the region. Tehran has sent an elite Revolutionary Guard commander to oversee part of the battle.

General Martin Dempsey, the top US military officer who visited Baghdad this week, told a Senate hearing on Wednesday that there was no doubt Islamic State would be pushed out of Tikrit, but he voiced concern about treatment of Sunni Muslims by the overwhelmingly Shi'ite attacking force.

"The question is what comes after, in terms of their willingness to let Sunni families move back into their neighborhoods, whether they work to restore the basic services that are going to be necessary, or whether it results in atrocities and retribution," he said.

Iraqi State television said Prime Minister Haider al-Abadi told military commanders and militia leaders they had a commitment to protect civilian life and property in Tikrit.

In Ramadi, about 90 km (55 miles) west of Baghdad, suicide car bombers in 13 vehicles attacked Iraqi army positions. The death toll from the attacks was not clear; officials rarely give details of casualties among security forces in Anbar.

A medical source said five people were killed in the attacks, but the real figure could be significantly higher.

One of the car bombs exploded near a bridge in the west of the city and damaged part of the bridge, a police source said.

An Islamic State suicide bomber also struck a position of the Kurdistan Workers' Party (PKK) in the northern town of Sinjar. After the bombing, some 70 militants launched an attack but were driven back by coalition air strikes, according to a senior Kurdish security official in the area.

In Baghdad, six people were killed when a car bomb exploded in a busy street in the mainly Shi'ite district of Hurriya. – Reuters