A Saudi jet has been reportedly shot down in northwestern Yemen as clashes near the Saudi Arabia-Yemen destroyed frontier crossing.

The F-16 fighter jet, flown on behalf of the Saudi-led coalition pounding Shi'ite Houthi rebels in Yemen, was brought down in Bani Harith district of the northern part of capital Sana'a.

According to Iran's state-run Press TV, two unexploded rockets were found inside the fighter aircraft, which was operating from Yemen's al-Dailami air base.

Sunni powerhouse Saudi Arabia and its allied forces have been carrying out airstrikes in Yemen against Houthi rebels, who are widely thought to be backed by Shi'ite-inclined Iran.

In another development, Saudi forces and Houthi militia have been trading heavy artillery fire near the border crossing.

Saudi Arabia shares a 1,800km-long porous border with Yemen.

The Haradh border crossing was partially destroyed during latest skirmishes, reported Reuters citing eye-witnesses.

The crossing, which is the largest for passenger and goods transit, was already evacuated before the shelling.

Residents in nearby towns also fled the area prior to the fighting.

The continuing turmoil has been raising serious concerns that regional powers - Shi'ite-inclined Iran, and the world's top oil exporter Saudi Arabia along with other Sunni Muslim states in the region - are throwing their weight behind the Houthi and the effectively-exiled Yemeni president Abd-Rabbu Mansour Hadi respectively.