* Fighting focused on outskirts of Qaeda-held Jaar
* Yemen, backed by U.S. drones, fighting militants in south
* Fears of al Qaeda rise near key shipping routes
ADEN, Yemen, May 19 (Reuters) - At least 22 al Qaeda-linked militants and 12 Yemeni soldiers were killed in clashes and air strikes overnight during a new U.S.-backed offensive against insurgents in the south of the country, officials said on Saturday.
Fighting erupted late on Friday and carried on into Saturday on the outskirts of the southern city of Jaar, held by Islamist militants, who have stepped up their campaign during months of political turmoil.
Government troops, backed by U.S. drone strikes, have been trying to push the insurgents out of strongholds in the south of the country, which lies near oil shipping routes through the Red Sea.
Washington and Yemen's neighbour Saudi Arabia both fear the instability in Yemen could give al Qaeda's regional wing a stronger foothold in the region.
"There is heavy fighting, and the armed elements are doing everything possible to stop the advance of (government) troops," a government official told Reuters, on condition of anonymity.
Government forces were about 1 km (0.6 mile) from Jaar, he added.
Twelve Yemeni soldiers and 17 militants were killed in the fighting and an air strike killed three militants on the outskirts of the city, the official said.
Another air strike destroyed a vehicle used by militants, killing two people inside in the southern province of Bayda, provincial governor Mohammed al-Ameri was quoted as saying on a defence ministry website.
Insurgents have seized swathes of territory in the south of the impoverished Arab country since mass protests erupted last year against then-President Ali Abdullah Saleh.
Washington has stepped up drone attacks in Yemen since President Abd-Rabbu Mansour Hadi took office in February. The Pentagon said earlier this month it had resumed sending military trainers to the Arab state.
On Friday, an army official and residents said troops backed by local tribesmen had killed 10 suspected Islamist militants outside Jaar.
Islamist militants linked to al Qaeda retreated on Thursday from the town of Lawder, about 80km north of Jaar, as warplanes attacked and ground troops advanced on insurgent-held towns.