Iraqi special forces have taken full control of a strategic university in eastern Mosul, according to senior commanders, the latest advance in a major push to drive ISIL out of its last urban stronghold in Iraq.

The capture of the Mosul University campus, seized by ISIL fighters when they took over the city in 2014, came after two days of intense clashes.

"Security forces have fully liberated the Mosul University," Talib Shaghati, the commander of the elite terrorism-combat service, told state TV on Saturday.

"The forces seized chemicals in the laboratories of the universities and defused explosives and car bombs," he added, without providing details.

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Used as a base by ISIL, also known as the Islamic State of Iraq and the Levant group or ISIS, the university complex lies in the north of the city on the east bank of the Tigris River, which splits Mosul in two.

Earlier on Saturday, bulldozers had smashed through a wall surrounding the sprawling campus and dozens of counterterrorism service troops sprinted through carrying rocket-propelled grenade launchers.

While they still came under heavy small arms fire, Iraqi soldiers at the university said ISIL resistance was significantly less than what they had faced during the first weeks of the Mosul operation.

"We were targeted with only four car bombs where before [ISIL] would send 20 in one day," special forces Lieutenant Zain al-Abadeen told the Associated Press news agency.

"And they aren't armoured like before. They're just using civilian cars."

Iraqi forces have now captured most districts in eastern Mosul, Iraq's second largest city.

Destroyed bridges

The massive push to retake Mosul from ISIL was launched on October 17.

The initial phase of the US-backed offensive saw a variety of forces, including Kurdish Peshmerga fighters, retake significant swaths of land in little time but the going has been tough inside the city itself.

New tactics employed since the turn of the year, including night raids and better defences against suicide car bombs, have given the campaign fresh momentum, according to US and Iraqi military officials.

The destruction of all bridges over the river in air strikes has also made it difficult for ISIL fighters in east Mosul to resupply or escape to the west bank, which they still fully control.

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US and Iraqi military officials say ISIL has further damaged at least two of them to try to hamper an army advance.

The western side of Mosul, which is home to the old city and some of the ISIL fighters' traditional bastions, was always tipped as likely to offer the most resistance.