ADEN, Yemen (Reuters) - Yemeni troops killed 10 suspected Islamist militants on the outskirts of the city of Jaar, an army official and residents said on Friday, in a new U.S.-backed offensive meant to reassert control in the south of the country.

Residents and a military official said fighting erupted overnight between insurgents and the Yemeni army backed by tribesmen on the northern outskirts of the city, which is held by al Qaeda linked militants. The clashes continued until Friday morning, killing ten militants, they said.

Residents in Jaar, in Abyan province, said they were told by the Yemeni military through loudspeakers on Thursday night to evacuate the city or head to secure areas as the army advances.

"Militants are digging bunkers and tunnels inside the city in preparation for fighting with the army," Mohammed Hussein, a resident of Jaar, said after he fled the city on Thursday.

On Thursday, militants linked to al Qaeda retreated from the town of Lawder, about 80 kms (50 miles) north of Jaar, as warplanes attacked and ground troops advanced on insurgent-held towns.

Washington has stepped up drone attacks in Yemen since President Abd-Rabbu Mansour Hadi took office in February, and the Pentagon said last week it had recently resumed sending military trainers to the Arab state.

Insurgents in the south of the impoverished Arab country exploited mass protests last year against then-President Ali Abdullah Saleh to seize large swathes of territory.

A growing Islamist insurgency in Yemen is of serious concern to the United States and oil exporter Saudi Arabia, who both fear that political infighting could give al Qaeda's regional wing a foothold near oil shipping routes through the Red Sea.

(Reporting by Mohammed Mukhashaf; Writing by Rania El Gamal)