SANA, Yemen - Yemen’s army pressed an offensive on Tuesday against southern towns held by Al Qaeda-linked fighters, with 11 militants and five soldiers killed in the clashes, military officials said.

Clashes around the town of Jaar, which fell to the militants more than a year ago, left eight Al Qaeda fighters and two soldiers dead over the past 24 hours, they said.

Another three Al Qaeda fighters and three soldiers were killed after militants ambushed an army supply column northeast of Zinjibar, the capital of Abyan Province.

Yemen’s army claims it has retaken most of Zinjibar, captured in 2011 by militants taking advantage of political turmoil to extend their control over large swaths of territory in the south.

The officials said the army continued its cautious advance toward the nearby town of Jaar supported by heavy airstrikes and artillery shelling.

They say militants are entrenched in the town and most of the civilian population has fled.

The officials spoke on condition of anonymity, in line with military regulations.

Residents who managed to flee Jaar said the army dropped fliers calling on citizens to stay away from combat zones.

“Jaar is a ghost town without electricity, water, and telephones, and not even one shop is open,’’ said Salim Bilal, 40, by telephone from the southern port city of Aden after he fled. He said people have to walk long distances to bring water from wells.

Militants set up antiaircraft guns and dug trenches in the streets and pulled their heavy weapons into the center of the town from the outskirts for fear of airstrikes, Bilal said.