Iraqi troops backed by US-led airstrikes have pushed deeper into eastern Mosul in a multi-pronged assault after a two-week lull in the operation to retake the Islamic State-held city.

Elite special forces pushed into the Karama and Quds neighbourhoods, while army troops and federal police advanced into the nearby areas of Intisar, Salam and Sumor. Smoke rose across the city as explosions and machine gun fire echoed through the streets.

Stiff resistance by the militants, civilians trapped inside their houses and bad weather have slowed advances in the more than two-month-old offensive to recapture Iraq’s second largest city, the extremist group’s last urban bastion in the country. It is the biggest Iraqi military operation since the 2003 US-led invasion.

Lt Gen Abdul-Wahab al-Saadi, commander of the special forces in eastern Mosul, said on Tuesday that his forces had been bolstered by reinforcements and were now less than two miles from the Tigris river which divides the city. A coalition airstrike this week destroyed the last remaining bridge over the river.

The special forces, officially known as the Counter Terrorism Service, have done most of the fighting, pushing in from the east. Regular army troops on the city’s south-east and northern edges, as well as militarised federal police further west, have not moved in weeks, unable to penetrate the city.

The troops have faced gruelling urban fighting, often going house to house against Isis militants who have had more than two years to dig in and prepare. Even in districts that have been recaptured, Iraqi troops have faced surprise attacks, shelling and car bombs. The extremists have launched more than 900 car bombs against Iraqi troops in and around Mosul.

Saadi said he expected Iraqi forces would drive Isis from Mosul and the rest of Nineveh province within three months. Iraqi leaders had previously vowed to drive the extremists from Mosul by the end of 2016.

Isis captured Mosul in the summer of 2014 when it swept across much of northern and central Iraq and the group’s leader declared the establishment of its self-styled caliphate from the pulpit of a Mosul mosque.

The city is still home to about a million people but roughly 120,000 have fled since the operation began on 17 October, according to the United Nations.