Iraqi forces’ hard-fought battle to retake the city of Tikrit from the Islamic State has “stalled” as the extremist group digs in, Pentagon spokesman Col. Steve Warren said Tuesday.

Warren attributed the situation to the forces -- the Iraqi Army and Iran-backed Shiite militias -- facing the complexities of urban combat and running into a “hardened and sophisticated defense” over the past several days. He said the Islamic State has "dug in."

The United States, which has led a coalition of countries to help defeat the Islamic State in Iraq and Syria, had largely stayed out of the battle for Tikrit, saying it has not been asked to help. 

However, a senior U.S. official said Tuesday, on the condition of anonymity, that the coalition is conducting surveillance flights over Tikrit, Saddam Hussein's hometown, and sending intelligence to Iraqi forces. 

Warren, asked about the matter, acknowledged Tuesday that the U.S. is “obviously” conducting surveillance operations throughout Iraq and Syria. But he declined to provide further details.

“I am not going to get into any of our ISR,” he said, using the acronym for intelligence, surveillance, reconnaissance, which is synonymous with drone operations. 

U.S. officials have largely stayed silent on the drone issue with regard to Tikrit, in part because Iran is involved in the Tikrit fight. U.S. officials have repeatedly said they are not in contact with Iranians in Iraq. 

Tikrit is about 80 miles north of Baghdad and one of the largest cities held by Islamic State militants. It lies on the road connecting Baghdad to Mosul. So retaking it would help Iraqi forces have a major supply link for a future operation to retake Mosul, the country's second-largest city.

The surveillance flights and the intelligence sharing that began Saturday marked the start of the coalition becoming involved in the offensive, which until now has largely been supported by Iranian advisers including Gen. Qassem Soleimani, commander of the powerful Revolutionary Guard Quds Force.

The official who spoke on the condition of anonymity said the support began at the request of the Iraqi government but declined to say whether coalition pilots are providing airstrikes.

A senior Iraqi military official said the coalition is not providing airstrikes in support of the Tikrit operation but launched strikes on Tuesday in the nearby oil refinery town of Beiji.

He also said that Soleimani has just left Tikrit after providing front-line assistance and advising since the start of the operation.

"He will come back if we need him to," said the Iraqi official.

Fox News’ Jennifer Griffin and Lucas Tomlinson and The Associated Press contributed to this report.