* Yemen trying to wrest control of south from Islamists
* Heavy overnight fighting near Jaar
* Twin air strikes on Jaar kill 16, including 6 civilians
* Zawahri calls on militants to fight for Islamic state (Adds al Qaeda leader remarks, updates toll)
By Mohammed Mukhashaf
ADEN, Yemen, May 15 (Reuters) - At least 44 people including 30 Islamist militants were killed overnight in Yemen, officials and residents said on Tuesday, as the government pressed ahead with a new U.S.-backed offensive against insurgents in the south.
The Islamist rebellion is of serious concern to the United States and to Yemen's much bigger neighbour Saudi Arabia, which both fear that instability could give al Qaeda's Yemen-based regional wing a bigger foothold near oil shipping routes through the Red Sea.
Residents and local officials said heavy fighting erupted late on Monday between the army and militants in an area called al-Jabalain in the south, as troops tried to advance on the militant-held city of Jaar.
The clashes continued until early on Tuesday, killing at least eight militants and one Yemeni soldier, they said, adding that the army had captured two Somali Islamist fighters.
Since the start of anti-government protests in early 2011, Islamist militants calling themselves Ansar al-Sharia (Partisans of Islamic Law) have expanded their influence in Yemen, seizing several towns and swathes of territory in the south.
Although the group is inspired by al Qaeda, the precise nature of their operational ties is unclear.
Both seek the application of Islamic law and Ansar al-Sharia this month said it had released more than 70 captured Yemeni soldiers on orders from Nasser al-Wuhayshi, the head of al Qaeda in the Arabian Peninsula (AQAP).
United Nations agencies and non-governmental organisations working in Yemen called in a statement on "involved parties to take all necessary steps to avoid civilian casualties and to minimise collateral damage".
ZAWAHRI CALLS FOR ISLAMIC STATE
In an Internet message on Tuesday, al Qaeda leader Ayman al-Zawahri said a power transition deal that eased long-ruling President Abdullah Saleh from power was a "great plot" by the United States and Western-allied Saudi Arabia to prevent Islamic militants from taking over in Yemen.
"All of the corrupt forces have agreed to fight the Mujahidden under the American flag and with Saudi funding," Zawahri said in the audio recording, posted on Islamist websites, whose authenticity could not be independently verified.
"The popular movement ... should be determined in cleansing the country from corrupt politicians who suck the people's blood like vampires ... and moving towards building a Muslim Yemen governed by God's law," he said.
On Tuesday morning, an air strike hit two suspected militant vehicles in Jaar, killing seven passengers and three others in a nearby house, residents said.
As people gathered to assess the damage, a second strike killed six of them, all civilians, the residents added.
Near the southern town of Lawdar, 12 militants, five government-allied tribal fighters, and two soldiers were killed in clashes in an area called Jebel Yasuf, according to a member of one of the tribal committees that have sprung up in the south to fill a security vacuum and fend off Islamist fighters.
Washington has also stepped up its drone attacks in Yemen since President Abd-Rabbu Mansour Hadi took office in February, and the Pentagon said last week it had resumed sending military trainers. (Writing by Rania El Gamal, Isabel Coles and Firouz Sedarat; Editing by Michael Roddy)