BAGHDAD - Thousands of Iraqi soldiers and militiamen sought to seal off Islamic State fighters in Tikrit and nearby towns on Tuesday, the second day of Iraq’s biggest offensive yet against a stronghold of the militants.

Iranian military commander Qassem Soleimani, who has helped coordinate Baghdad’s counter-attacks against Islamic State since it seized much of northern Iraq in June, was overseeing at least part of the operation, witnesses told Reuters.

His presence on the frontline highlights neighbouring Iran’s influence over the  fighters who have been key to containing the militants in Iraq.

In contrast the US-led air coalition which has been attacking Islamic State across Iraq and Syria has not yet played a role in Tikrit, the Pentagon said on Monday, perhaps in part because of the high-level Iranian presence.

Iraqi military officials said security forces backed by the  militia known as Hashid Shaabi (Popular Mobilisation) units were advancing gradually, their progress slowed by roadside bombs and snipers.

They have yet to enter Tikrit, best known as the hometown of executed former president Saddam Hussein, or the nearby Tigris river town of al-Dour, which officials describe as a major centre for the Islamic State fighters.

On the southern flank of the offensive, army and police officials said government forces moving north from the city of Samarra could launch an attack on al-Dour later on Tuesday.

Soleimani, head of the Iranian Revolutionary Guards Quds Force, was directing operations on the eastern flank from a village about 55 km (35 miles) from Tikrit called Albu Rayash, captured from Islamic State two days ago.

With him were two Iraqi paramilitary leaders: the leader of the Hashid Shaabi, Abu Mahdi al-Mohandis, and Hadi al-Amiri who leads the Badr Organisation, a powerful militia. “(Soleimani) was standing on top of a hill pointing with his hands towards the areas where Islamic State are still operating,” said a witness who was accompanying security forces near Albu Rayash.

The offensive is the biggest military operation in the Salahuddin region north of Baghdad since last summer, when Islamic State fighters killed hundreds of Iraq army soldiers who had abandoned their military base at Camp Speicher outside Tikrit.

Several Hashid Shaabi fighters have described this week’s campaign as revenge for the Speicher killings. Prime Minister Haider al-Abadi has urged them to protect civilians in Salahuddin province. The drive follows several failed attempts to push the militants out of Tikrit. Since Islamic State declared a caliphate last year in territories under its control in Iraq and Syria, Iraqi forces have not managed to recapture and control a single city.

Meanwhile, Australia announced Tuesday it will send another 300 troops to Iraq in a joint mission with New Zealand to help train local forces fighting to reclaim territory seized by the Islamic State group.

The decision follows Wellington last week deciding to deploy some 140 soldiers in a non-combat role to boost the Iraqi military’s ability to battle the militants.

Prime Minister Tony Abbott said the decision followed a formal request from the Iraqi and US governments with the mission intended to span two years.

“I want to stress that we haven’t taken this decision lightly. Ultimately, it is Iraq that must defeat the death cult (Islamic State) but we do not want to leave the Iraqis on their own,” he told reporters. “We are naturally reluctant as a peace-loving people to reach out to far-away conflicts but, as we know, this conflict has been reaching out to us for months now.” The move came as some 30,000 Iraqi troops and militia backed by aircraft pounded militants in and around Tikrit in the biggest offensive yet to retake one of the Islamic State group’s main strongholds in the country.

The operation is the broadest since IS overran swathes of the country last year and is seen as a step towards the liberation of Mosul, the militants’ main hub in Iraq.

Some 170 Australian special forces are already in Iraq helping to train government troops, and Abbott said it was in his country’s national interest to bolster their presence.

He said about 100 Australians were fighting with Islamic State and other terrorist groups in Syria and Iraq.