Iraqi forces pressed deeper into one of the Islamic State’s key strongholds Thursday, further challenging the militants’ hold on the city of Tikrit in a decisive battle that could set the stage for a wider offensive for control of northern Iraq.

The showdown in Tikrit — waged without significant American air support — is also a test of coordination between government-led Sunni forces and Shiite militias backed by Iran. The two groups have often been at odds but have joined forces against the common enemy of the Islamic State.

Rocket and mortar fire could be heard coming from Tikrit, the home town of former strongman Saddam Hussein, as Iraqi security forces sought to drive back Islamic State fighters in street-by-street combat.

Iraqi troops and allied Shiite militiamen entered Tikrit on Wednesday on two fronts, pushing through bomb-rigged defenses set up by the Islamic State, which seized Tikrit in June as part of a blitz-style advance through northern Iraq.

[ Read: The Islamic State appears to be fraying from within ]

The gains by Iraqi forces could mark a crucial step in dislodging the Islamic State from other key areas, including the northern city of Mosul.

But it was unclear whether Iraqi forces­ would hold their ground in Tikrit, which straddles an important highway junction about 110 miles northwest of Baghdad. Government troops have struggled to maintain control over recaptured territory in the past.

The Islamic State, meanwhile, has gone on the offensive in other areas, including Ramadi in western Iraq and in the oil-rich territory in eastern Syria.

The head of the military operation told the Associated Press that troops would try to reach the city center on Thursday. The official spoke anonymously, the AP said, as he is not authorized to brief media.

Iraqi television showed civilians in towns near Tikrit greeting pro-government forces­ as they swept through on their way to the city.

The military offensive includes a combined force of up to 30,000 troops, including a large contingent of Shiite militia fighters. Some officials and rights advocates have raised concerns about the sectarian nature of the operation and the possibility of retaliatory attacks against the local population, which is mostly Sunni.

Sunnis — who dominated Iraq under Hussein’s regime although they are a minority in the country — have complained they now face discrimination and abuses at the hands of the Shiite-led government. Some Sunnis had initially backed the Islamic State to counter Shiite power.

Tikrit also has powerful symbolism for Shiites: It was the site of a massacre of as many as 1,700 Shiite soldiers in late spring by militants of the Islamic State, a radical al-Qaeda offshoot that is also known as ISIS or ISIL.

Shiite commanders have portrayed the current offensive as revenge for the slaughter, in which some local Sunni tribes also participated.

In Washington, the Obama administration hailed the Tikrit operation as proof that its broader strategy in the region was working.

White House press secretary Josh Earnest said the Islamic State has been pushed out of 25 percent of the territory that its fighters took in the spring and summer in Iraq. He apparently was also referring to defeats suffered by the extremist Sunni combatants in Diyala province, just northeast of Baghdad, and in Kurdish areas near Mosul.

But the absence of U.S. warplanes in the Tikrit offensive appeared to expose rifts in the U.S.-Iraqi alliance. Iraqi officials have suggested that American air power was not necessary in the offensive, which began March 1.

U.S. planes have been striking Islamic State targets elsewhere in the country. The United States is also helping train Iraqi military units and has deployed about 300 advisers to al-Asad Air Base in the western province of Anbar.

Gen. Martin E. Dempsey, chairman of the Joint Chiefs of Staff, acknowledged Wednesday that Iranian-backed Shiite militia forces­ “dramatically” outnumbered Iraqi military and Sunni volunteer forces­ participating in the battle for Tikrit.

He said the pro-government side included about 1,000 Sunni tribal members, a brigade of 3,000 Iraqi troops, several hundred Iraqi military counter­terrorism forces­, and “approximately 20,000 of the popular mobilization force, which are the Shia militia.”

[Read: U.S. commanders seek bigger tests beyond Tikrit]

Dempsey, speaking in congressional testimony, said that Iranian participation in Iraq was “a positive thing in military terms against ISIL.”

But, he said, “we are all concerned about what happens after the drums stop beating and ISIL is defeated, and whether the government of Iraq will remain on a path to provide an inclusive government for all of the groups within it. We’re very concerned about that.”

The Tikrit operation, he said, “will be a strategic inflection point one way or the other in terms of easing our concerns or increasing them.”

Another senior U.S. official expressed concern about the prominent role being played by Iran and its proxies, which he said was especially worrisome to the Persian Gulf Arab allies in the U.S.-led coalition battling the Islamic State.

“They are deeply concerned . . . that Iran is taking a stab at eliminating our contribution or minimizing it,” said the official, who spoke on the condition of anonymity to discuss sensitive diplomatic matters. “There is a concern over the struggle between the United States and Iran for strategic influence and lasting influence.”

But even if Iraqi forces can hold Tikrit, they face a prolonged insurgency in the area, analysts say. That will have implications for operations to retake Mosul, a city of about 1 million people still under the control of the Islamic State.

For months, government troops have been mired in seesaw battles with Sunni militants in areas of Anbar province, as well as the oil refinery town of Baiji, about 27 miles northwest of Tikrit. Iraqi forces­ seized Baiji in November but later ceded ground when the jihadists mounted a successful counter­offensive.

Iraqi security expert Safa al-Asam said pro-government forces­ were not trained for urban warfare and ran the risk of getting bogged down in a guerrilla-style conflict with the militants in Tikrit.

If the Shiite militias also stay on to fight the militants, their presence could increase tension with local Sunni tribes.

“There will be major problems,” Iraqi analyst Hisham al-Hashimi said of the militias. “I believe there will be assassinations and human rights violations. They will not leave land they liberated with their own blood.”

On Thursday, Iraqi Prime Minister Haider al-Abadi called on Iraqi forces and militias to closely supervise their troops to ensure no abuses are committed in Tikrit.

Daniela Deane in London, Greg Jaffe and Karen DeYoung in Washington and Mustafa Salim in Baghdad contributed to this report.

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