ADEN (Reuters) - Heavy fighting erupted in southern Yemen near Aden airport on Friday when local militia attacked Shi'ite Houthi rebels in a push to drive them from the district, residents and fighters said.

Saudi-led forces also made four air strikes on a military base near the airport, a source in the southern militia told Reuters.

A Saudi-led coalition began air strikes in Yemen on March 26 in a campaign to restore Yemeni President Abd-Rabbu Mansour Hadi to power. He fled in March, after Iranian-backed Houthi rebels seized the capital Sanaa in September and then thrust into central and south Yemen.

Aden is Yemen's commercial hub. Its airport has been closed since fighting began but its port provides sporadic access for desperately needed humanitarian aid to enter the country.

Houthis and forces loyal to former president Ali Abdullah Saleh are concentrated around Aden's districts of Khor Maksar, Crater and Moalla.

The fighting in Khor Maksar has killed four southern militia fighters and 15 Houthis so far, the militia source said.

Later on Friday Houthis fired shells at Saudi Arabia's southwestern province of Jizan, according to their official Twitter account. There was no immediate information about casualties.

Saudi forces and the Houthis have been trading fire across the border since the Arab alliance began its military operations.

On Thursday, two Saudi border guards were killed and five wounded by shells fired from Yemen.

Intense air raids by the Arab alliance were also reported overnight by residents of Saada, a province in northwest Yemen which borders Saudi Arabia. Raids also targeted a weapons storage site in Sanaa, said residents.

On Monday, Houthi fighters suffered their first significant setback in the south in two months of civil war when local militia ejected them from much of the southern city of Dalea, about 170 km (105 miles) north of Aden.

The militias, who call themselves the Southern Resistance, are a loosely allied group of fighters who took up arms against the Houthis.

U.N.-sponsored peace talks set to be held in Geneva this week have been postponed because of the heavy fighting.

(Reporting By Mohammed Mukhashaf; additional reporting by Mohammed Ghobari in Cairo; Writing By Maha El Dahan; Editing by Mark Trevelyan)