Iraqi government forces and their allied militia have entered parts of Tikrit, as they continue a major offensive to recapture the strategic city from the Islamic State of Iraq and the Levant (ISIL).

Analysis: Liberators or Invaders? The Iraqi armed forces and the Popular Mobilisation Forces offensive to retake Tikrit from ISIL is as strategically significant as it is politically charged. Strategically, Tikrit will prove to be a test of wills and a preview of future battles. How the fight goes and how it ends will have major ramifications on the rest or Iraq, most notably the fight for Mosul. Taking over Tikrit will prove costly, especially to its resident who fought bravely and suffered gravely during the 2003 invasion of Iraq. Its association with the former leader, Saddam Hussein al-Tikriti, does not go unnoticed. Click here to read the full analysis by Marwan Bishara, Al Jazeera senior political analyst

Iraq's defence ministry said on Tuesday that its forces have surrounded the city along the Tigris River, and are preparing to advance into the city.

Government troops and Shia volunteer fighters from Popular Mobilisation Forces are now reportedly stationed in the main streets of the city, as they started to advance towards al-Qadisiah Street, the defence ministry statement said.

Al Jazeera's Jane Arraf, reporting from the Kurdish city of Erbil, quoted sources as saying that Iraqi forces are now holding parts of the city.

"But that doesn't mean they have control of the entire city," our correspondent said, adding that ISIL fighters have reportedly blown up a bridge leading to Tikrit.

Several roads into the city are also reportedly rigged with explosives.

Earlier, an Iraqi defence ministry video showed Iraqi forces destroying 20 heavy machine guns, and 20 vehicles as it advanced into Tikrit.

At least 382 improvised explosive devices were also reportedly dismantled.

The same video claimed that government troops have killed 350 suspected ISIL fighters within four days of its ongoing operation in the area. Al Jazeera could not independently verify the ISIL death toll.

Sectarian tension

The battle over Tikrit, a Sunni stronghold, is crucial for Iraqi forces in their advance towards Mosul, Iraq's second largest city, which is controlled by ISIL.

Tikrit serves as an important hub because it is on the main highway leading to Baghdad.

But the advance of government forces and Shia militias into Tikrit has also ignited sectarian tensions.

On Tuesday, Iraqi Shia cleric Muqtada al-Sadr issued a statement urging the Iraqi government to investigate and punish anyone using "excessive violence" against the Sunni residents from areas recently liberated from ISIL.

The statement comes after reprisal attacks in al-Ojail, where fighters from an armed group, the League of the Righteous headed by Qais al-Khazali, reportedly ransacked and burned houses belonging to Sunni residents.

Al-Khazali had said that his group was working under the guidance of Iranian General Qassem Soleimani, the commander of the elite Quds Brigade, who has been seen directing operations on the eastern flank of Tikrit.

In the last few days, Iraqi forces and Shia militia have captured several towns in the outskirts of Tikrit, including al-Alam and al-Dour.

Government troops have also reportedly taken control of the oil fields in al-Ojail, another town near Tikrit.

More troops are also reportedly standing by further out, in Samarra and Beiji, as well as outside the town of Garma in Anbar Province.

The Iraqi government is hoping that victory in Tikrit will help persuade Sunnis in other places to rise up against the ISIL, as the operation proceeds further north into Mosul.