KABUL, Afghanistan — Another district in the embattled southern province of Helmand fell to the Taliban on Tuesday, Afghan government officials said, adding important new territory to the insurgents’ control.

A large number of Taliban fighters attacked the government center in Khan Neshin District late Monday night, with heavy firefights continuing until 5 a.m. Tuesday, when government defenders finally fled, according to Col. Allah Dad. Colonel Dad is the commander of the Fourth Battalion of the Afghan Border Police, which was in charge of the area.

Khan Neshin became the fifth of Helmand’s 14 districts in which the government centers have fallen to the Taliban, mostly in recent months as a result of fighting that has continued at an intense pace through the winter. In at least two other districts, including Sangin and Kajaki, the Taliban control most of the territory except the government centers and are very active in at least four others, including part of the provincial capital. By many accounts, the insurgents control more than half of the provincial territory, and dominate much of the rest.

The Taliban advances have come despite stepped-up airstrikes by American warplanes in crucial districts, as well as involvement by American Special Operations force s on the ground. Last month, a new battalion of American soldiers, believed to number as many as 700, was sent to Helmand to provide support for Special Operations forces operating in the area, the United States military said. It was the largest new deployment of American soldiers outside a major base since the official end of the combat mission in December 2014.