BAGHDAD — A month after liberating Mosul from the Islamic State, Iraqi forces began a new offensive Sunday to retake Tal Afar, one of the last big cities in Iraq under control of the extremists.

As he has done frequently during the three-year military campaign against the Islamic State, Prime Minister Haider al-Abadi appeared on state television in the dark hours — close to 3 a.m. Sunday, a time chosen to heighten the drama — wearing a black uniform in the style of Iraqi special forces to announce that the operation had begun.

Using an Arabic acronym for the Islamic State, Mr. Abadi addressed the militants directly. “I would say to Daesh fighters, you have no choice: Either surrender or die,” he said.

Tal Afar, once a remote military outpost for the Ottoman Empire, fell to the Islamic State in 2014. It was strategically significant for its location along a supply route between Mosul and Syria, where the militant group, also known as ISIS or ISIL, is also on its heels as it defends its de facto capital there, Raqqa.