Iran proposed a peace plan for Yemen on Tuesday and called for an end to Saudi-led air strikes against Houthi rebels allied to Tehran, but the move was likely to draw a cool response from Riyadh.

On the battlefront, militiamen loyal to deposed President President Abd-Rabbu Mansour Hadi said they had pushed back Houthi fighters at several points in southern Yemen, including districts of the port city of Aden, the focal point of a conflict that entered its most dangerous phase three weeks ago.

After prolonged street fighting, Houthi fighters withdrew from Aden's Khor Maksar district, where the international airport and foreign missions are located.

The pull-out deprives the Houthis of a bridge to downtown areas where they face heavy resistance from local fighters.

Saudi Arabia and its Sunni Arab allies have been bombing the Houthis since March 25 to drive them from Aden, the most important city still loyal to Hadi.

The Houthis, northern-based Shi'ite Moslems, seized control of Yemen's capital Sanaa in September, confining Hadi to the presidential residence. He fled to Aden in February then escaped to Riyadh last month as Houthi forces closed in on the city.

The conflict, though rooted in local rivalries, has become a proxy battlefield for regional powers Sunni-ruled Saudi and mainly Shi'ite Iran. Saudi Arabia and other powers accuse Iran of arming the Houthis and interfering in Yemeni affairs. Tehran denies giving military support to the Houthis.

Iranian Foreign Minister Mohammad Javad Zarif, speaking in Madrid on Tuesday, put forward a peace proposal involving a ceasefire, humanitarian assistance, a dialogue between Yemeni factions, and a broad-based government.