RIYADH - A mortar shell fired by Yemen’s Houthi militia across the border into Saudi Arabia killed three of the kingdom’s army officers on Friday, a Defence Ministry statement carried by the Saudi state news agency SPA said on Saturday.

The statement said more than 500 Houthi fighters have been killed in clashes on the border since the conflict began on March 26, but did not say how it came by that figure. Three Saudi Arabian border guards were killed last week.

Earlier, local militiamen in the Yemeni city of Aden said they captured two Iranian military officers advising Houthi rebels during fighting.

Tehran has denied providing military support for Houthi fighters, whose advances have drawn air strikes by a regional coalition led by Saudi Arabia, the Islamic Republic’s main rival for influence in the Gulf.

If confirmed, the presence of two Iranian officers, who the local militiamen said were from an elite unit of Iran’s Revolutionary Guards, would further worsen relations between Tehran and Riyadh who are vying for dominance in the region.

A Houthi mortar shell fired into Saudi territory on Friday killed three officers and injured two others, a statement from the kingdom’s Defence Ministry carried by state media said on Saturday, bringing Saudi casualties in the conflict to six.

Three sources in the southern port city’s anti-Houthi militias said the Iranians, identified as a colonel and a captain, were seized in two separate districts that have been rocked by heavy gun battles.

"The initial investigation revealed that they are from the Quds Force and are working as advisors to the Houthi militia," one of the sources told Reuters.

"They have been put in a safe place and we will turn them over to (the Saudi-led coalition) Decisive Storm to deal with them."

Saudi-led air strikes, entering their third week, hit Houthi and military targets throughout the country on Saturday, pounding government buildings and a presidential palace used by the group's leaders in the Red Sea port city of Hodaida.

Ground combat between armed factions battered southern Yemen, killing around 20 Houthi fighters and two rival militiamen, residents and militia fighters said.

Bolstered by the air raids, local armed groups have been resisting the southward advance of the northern-based Shi'ite Muslim Houthis.