Yemen presses ahead with offensive on militants

* Army says airstrikes killed at least 30 militants

* Militants say U.S. drones conducted the attacks

* Say none of their fighters were killed or hurt

JAAR, Yemen, June 13 (Reuters) - Yemen on Wednesday pressed ahead with a U.S.-backed offensive to drive al Qaeda-linked insurgents from the country's south, a day after the army notched up its biggest victory in more than a year by recapturing two strategic cities.

Three airstrikes targeted areas held by militants inside and outside of the town of Azzan, killing at least 30 fighters and wounding dozens more, Colonel Ahmed al-Maqdashi, head of security in Shabwa province, said in statement posted on the Defence Ministry's website.

The attacks appeared to underscore the army's determination to press home its advantage after recapturing the cities of Jaar and Zinjibar on Tuesday, forcing hundreds of Islamist fighters to flee.

It was not immediately clear if Wednesday's strikes were carried out by Yemeni warplanes or U.S. drones. One local official in Azzan said at least one strike was by a drone.

Washington has repeatedly used drones to target Yemeni militants in order to try to contain a threat it has been urging the government to take more seriously.

Ansar al-Sharia (Partisans of Islamic Law), an offshoot of al Qaeda in Yemen, said in a statement that U.S. drones had launched five attacks in Azzan on Wednesday morning. It denied any of its fighters had been killed or wounded.

The recapture of Jaar and Zinjibar was the army's most significant victory against the militants in more than a year of political turmoil that has taken Yemen to the brink of civil war and fuelled fears about al Qaeda's presence in a country that is next door to Saudi Arabia, the world's top oil exporter.

Some residents of the two wrecked cities began to return to their homes on Wednesday.

Emboldened by waning government control over the impoverished country during last year's popular protests that ousted former President Ali Abdullah Saleh, militants seized Jaar in March 2011, before occupying Zinjibar and the coastal town of Shaqra.

U.S. officials say that President Abd-Rabbu Mansour Hadi - who came to power in February after Saleh signed a power transfer deal brokered by the Gulf states - is more cooperative in the fight against Islamist militancy than his predecessor.

Al Qaeda in the Arabian Peninsula (AQAP) is believed to be the most active branch of the global network and has plotted a number of botched attempts against U.S. targets. (Reporting by Mohammed Mukhashaf; Writing by Rania El Gamal; Editing by Andrew Osborn)