Dozens of Houthi fighters were killed in clashes with Saudi forces on Yemen's northern border, Riyadh said on Thursday, while air strikes and artillery fire rocked the southern city of Aden in fighting residents said was the worst in over a month of war.

Three Saudi soldiers were killed in the fighting, which began when Houthis attacked a border post in Najran province and were repulsed, Riyadh's Defence Ministry said.

Earlier, the Interior Ministry said a border guard was killed by a shell while on patrol in a different area, bringing the number of Saudi casualties in the five-week campaign to 14.

The Iran-allied Houthi rebels and local militiamen also traded tank and mortar salvos in Aden's Khor Maksar district near the airport from Wednesday into Thursday and warplanes from a Saudi-led coalition of Arab states bombed Houthi positions.

In the capital Sanaa, new air strikes by the Saudi-led coalition hit the airport days after jets bombed the runway to stop an Iranian plane landing, an airport official said. Damage to the airport has stopped aid deliveries, officials said.

Residents in Aden said dozens of families had fled, braving Houthi sniper fire and checkpoints as homes were shelled and burned.

"The scene is disastrous, not just in the streets where fighting is going on but inside houses where families are often trapped and terrified," local activist Ahmed Al-Awgari said.

"Women and children have been burnt in their homes, civilians have been shot in the streets or blown up by tank fire," he said.

Scores of residents and fighters from both sides have been killed throughout the conflict, and residents said at least six Houthis and two local militiamen were killed overnight.

The Houthis hail from Yemen's far north and belong to the Zaydi sect of Shi'ite Islam. They swept into the capital Sanaa in September and pushed south and east, saying they were winning a revolution against Sunni militants and corrupt officials.

But their push into the outskirts of the southern city of Aden on March 25 triggered a Saudi-led air campaign to drive them back and aid local fighters.

The Sunni kingdom believes the Houthi group is a proxy for Shi'ite Iran, and Saudi backing for the resistance in Yemen's mostly Sunni south has raised fears that Yemen could descend into all-out sectarian war.

Militant Sunni groups have consolidated their position in eastern parts of Yemen since the fighting began and on Thursday an Islamic State group in the country released a film it said showed the killing of 14 Yemeni soldiers, the SITE Intelligence monitoring service reported. - Reuters