Yemeni army kills 33 militants in south

* Yemen has become base for al Qaeda

* Army says among dead were Somali, Egyptian

* Army has offensive to take back areas of south (Adds name of Sanaa bomber)

ADEN, May 24 (Reuters) - Yemeni troops fought Islamist militants in southern cities on Thursday, as the government pressed ahead with a U.S.-backed offensive to help stabilise the impoverished Arab state that has turned into a base for al Qaeda.

At least 33 militants were killed in heavy fighting with the Yemeni army on the western outskirts of the city of Jaar, in southern Abyan province, army officials and residents said. Among the dead were a Somali and an Egyptian fighting with the insurgents, they said.

Yemeni warplanes also launched strikes on Jaar, but no casualties have been reported, residents said.

Western and Gulf Arab countries have watched with mounting alarm as a political crisis in Yemen has given al Qaeda the opportunity to develop a base from which to launch attacks around the world.

Insurgents in the south exploited mass protests last year against former President Ali Abdullah Saleh to seize large swathes of territory.

In the strategically important city of Zinjibar, Islamist militants on Thursday launched a counter-attack against government forces from the eastern parts of the city but were pushed back, a local army official said. One soldier was wounded in the fighting.

The Yemeni army recaptured parts of the southern city of Zinjibar on Wednesday.

The advance of troops into the centre and northern neighbourhoods of Zinjibar, the capital of Abyan province, represents a new front in the government's offensive to reclaim areas seized by insurgents in the south.

The militants have given shelter and support to al Qaeda's regional wing, which on Monday killed 100 soldiers in a suicide bombing at a military parade in the capital Sanaa.

On Thursday, Ansar al-Sharia, a militant group affiliated to al Qaeda, said in a mobile text message that the Sanaa suicide bomber's name was Haitham Hameed Hussein Mefreh, a soldier in the Yemeni army.

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

The United States and Saudi Arabia have come to regard Yemen-based al Qaeda in the Arabian Peninsula, known as AQAP, as the network's most dangerous wing.

Early in May, Washington said Western and Arab intelligence agencies had foiled a plot to arm a suicide bomber with an improved version of an underwear bomb that failed to explode on a 2009 U.S.-bound flight. (Reporting by Mohammed Mukhashaf; Writing by Rania El Gamal; Editing by Pravin Char)