IRBIL, Iraq — Iraqi security forces and Iranian-backed Shiite Muslim militias on Tuesday pushed to the outskirts of the encircled city of Tikrit, residents and Iraqi officials said, after 10 days of heavy fighting that have seen government-aligned forces take control of two key towns north and south of the city.

News that government forces had arrived on the outskirts of Tikrit, which has been occupied by the Islamic State group since last summer, was greeted triumphantly on state television, with officials claiming the militants had withdrawn from the city and predicting a quick victory.

But officials have made similar claims in the past about the success of operations against the Islamic State — last summer about a failed mission to retake Tikrit, and most notably last fall about the town of Baiji — only to see the gains they claimed evaporate before fierce counterattacks.

The Salahuddin Operations Center, which is overseeing the operation, said Tuesday night that pro-government forces, including a small number of Sunni Muslim tribal fighters, had surrounded the city and security forces had taken control of the city’s hospital on the southern edge of the town.

But Islamic State militants dynamited a bridge east of the city, preventing pro-government forces that had earlier captured the towns of al Dour and al Alam from crossing the Tigris River to support government forces driving from the south. The government also holds a military base west of the city.

State television and government news services provided video and still pictures of multiple locations in al Alam and al Dour that appeared to verify government control, but notably they aired nothing that indicated troops had reached Tikrit proper.

Capturing the town would be a symbolic victory for the Shiite-led government in Baghdad, marking not only the most important advance against the Islamic State since last June, when the jihadists captured the country’s second-largest city, Mosul, but also installing Iranian-backed militias in the hometown of Saddam Hussein, the late Iraqi leader who fought a brutal war against Iran in the 1980s and was reviled by most Shiites, Iraq’s majority sect.