People stand on the rubble of houses destroyed by an air strike near Sanaa Airport March 31, 2015. REUTERS/Khaled Abdullah

ADEN, Yemen (Reuters) - Yemen’s Houthi militiamen and allied army units shelled Aden overnight while Saudi-led coalition jets bombed their positions near the airport, killing at least 36 people, officials and witnesses said on Tuesday.

Iran-allied Houthis are pushing on the outskirts of the city, the last bastion of Yemeni President Abd-Rabbu Mansour Hadi, despite six days of Saudi-led air strikes meant to stem their advance.

Artillery fire on the Khor Maksar district of Aden killed 26 people overnight, a health ministry official said.

Shells hit a residential building in the area close to a private residence once used by Hadi -- who is now abroad in Saudi Arabia -- killing ten militiamen loyal to the president, a witness told Reuters.

Coalition planes bombed Houthi fighters and their army allies in the area of the airport, which has traded hands between the two warring sides during over a week of heavy fighting. It was not immediately clear if there were any casualties.

Residents of the city reported shops were shuttered and streets were deserted for fear of worsening security.

In the southern province of Dhalea, Hadi loyalists, who were backed up by five coalition air strikes on Tuesday, reported heavy shelling and street fighting with the Houthis and their allies.