IRBIL, Iraq - Iraqi security forces backed by Sunni and Shiite Muslim militias cautiously pushed Tuesday into the center of the besieged city of Tikrit, taking control of key government buildings on the southeastern edge of the town from Islamic State militants who have controlled the city for nearly a year.

Iraqi Prime Minister Haider al-Abadi announced that the city's western and southern portions had been liberated, but military commanders involved in the operation warned that at least three neighborhoods and a palace complex defended by hundreds of Islamic State fighters remained out of government hands.

In Washington, the Pentagon took a cautious view of developments. "We welcome the progress by Iraqi forces in Tikrit today and are consulting with our Iraqi partners to continue efforts toward the full liberation of the city," an official statement said.

"Our security forces have reached the center of Tikrit, and they have liberated the southern and western sides, and they are moving towards the control of the whole city," al-Abadi said in a statement issued to state television. Among the locations that Iraqi troops captured was the provincial government compound and an adjacent palace complex that had once been a residence for late Iraqi dictator Saddam Hussein. Both had been key Islamic State fortifications.

Fighting, however, was expected to continue. Even as al-Abadi was declaring liberation, other officials pointed out that the Islamic State group continued to deploy suicide bombers and snipers even in areas government troops had entered.

Still, a military official at the command center outside the city hailed Tuesday's developments as the most substantial progress in the monthlong campaign and credited U.S. airstrikes over the last week with degrading Islamic State defenses at the government and palace complex. He asked not to be identified because he was not authorized to speak to journalists.

"The operation was a success after the airstrikes did what they were intended to do," he said by phone. "They broke down Daash's defenses around Saddam's palace and the governor's compound that had been blocking access to the center of the city from the south and east." Daash is an Arabic acronym for the Islamic State group, which is also known as ISIS or ISIL.

When asked whether Shiite militias, many trained and led by Iranian advisers, had participated in the effort despite U.S. demands that they withdraw in exchange for U.S. air support, the official chuckled.

"Many patriotic units and volunteers, both Sunni and Shiite, are participating in the operation," he said. "It is not clear if the prime minister will request additional airstrikes for the rest of the operation now that we have entered the city itself."