Shi'ite fighters known as Hashid Shaabi carry their weapons on the southern edge of Tikrit March 12, 2015. Iraqi security forces and mainly Shi'ite 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. [Photo/Agencies]

TIKRIT, Iraq - Iraqi troops clashed along two fronts with Islamic State militants in Tikrit on Thursday as rockets and mortars echoed across Saddam Hussein's hometown a day after soldiers and allied Shiite militiamen swept into this Sunni city north of Baghdad.

Iraqi forces entered Tikrit for the first time on Wednesday from the north and south. On Thursday, they were fighting their way through the city and expected to reach the center within three to four days, according to Lt. General Abdul-Wahab al-Saadi, the commander of the Tikrit operation.

The IS militants were trying to repel the Iraqi forces with snipers, suicide car bombs, heavy machine guns and mortars, said al-Saadi, speaking to The Associated Press at the front-lines.

Tikrit, the capital of Salahuddin province, sits on the Tigris River about 130 kilometers (80 miles) north of Baghdad. Several of Saddam's palaces remain there.

Iraqi Defense Minister Khaled al-Obeidi, who was also at the front-line on Thursday, told the AP that the operation to retake Tikrit is "essential to opening a corridor for security forces to move from the south to Mosul," he said, referring to Iraq's second-largest city and the militants' biggest stronghold.

He described the operation as "100% Iraqi, from the air and ground."

When the Islamic State last year swept into Mosul, the US-trained Iraqi military crumbled and the militants seized tanks, missile launchers and ammunition, steamrolling across northern Iraq. The CIA estimates the Sunni militant group has access to between 20,000 and 31,000 fighters in Iraq and Syria. Military officials believe there may about 150 foreign fighters with the IS inside Tikrit, including fighters from Chechnya and the Arab Gulf countries.

Iraqi officials now say that at least 30,000 men - including the military, militias, Sunni tribes and police - are fighting to capture Tikrit.

US Gen. Martin Dempsey, the Joint Chiefs chairman, said Wednesday that at least 20,000 militiamen are taking part in the Tikrit fighting.