BEIRUT — U.S.-backed fighters in Syria converged from three sides on an Islamic State stronghold near the Turkish border Thursday, while Iraqi special forces pushed deeper into Fallujah, one of the last bastions of the militant group in western Iraq.

In Libya, Islamic State militants were fleeing their stronghold of Sirte as forces loyal to a U.N.-brokered government advanced, with some fighters cutting off beards and long hair to blend in with civilians.

The anti-Islamic State offensives posed a significant challenge to the extremist group as it tried to stave off multiple attacks across parts of Syria and Iraq, where it declared a so-called caliphate in 2014, and in more recently seized territory in chaotic Libya.

If the U.S.-backed Syria Democratic Forces capture Manbij, it will be the biggest strategic defeat for the Islamic State in Syria since July 2015, when it lost the border town of Tal Abyad, a major supply route to the militants’ de facto capital of Raqqa.

Manbij, which had a prewar population of 100,000, is one of the largest Islamic State-held urban areas in northern Aleppo province and is a waypoint on an Islamic State supply line between Raqqa and the Turkish frontier.

In a sign of the town’s perceived significance, the Syrians’ advances were accompanied by intense airstrikes from the U.S.-led coalition battling the militants. The U.S. Central Command said the coalition has conducted more than 105 strikes in support of the battle to liberate Manbij.