BAGHDAD — Iraqi security forces and mainly Shiite militia exchanged fire sporadically with Islamic State fighters in Tikrit on Thursday, a day after they pushed into Saddam Hussein’s home city in their biggest offensive yet against the militants.

A source at the local military command reported intermittent gunfire in the morning as the army and militia fighters struggled to advance in the southern, northern and northwestern parts of the city which they took in the last 24 hours. 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. The military source said the insurgents still held the presidential complex and at least three other districts in the centre of Tikrit, holding up further army advances with snipers and bombs. A Reuters photographer saw one car bomb explode on the southern edge of the city, and security officials say Islamic State fighters have booby-trapped abandoned buildings. — Reuters