Thousands of Shi'ite Muslim Houthi fighters, who control much of Yemen, held military exercises near the border with top oil exporter and Sunni power Saudi Arabia on Thursday, a Houthi commander said, adding to fears Yemen's chaos could deepen.

The rise to power of the Iran-backed Houthis since September has deepened divisions in Yemen's already complex web of political and religious allegiances, and left it increasingly cut off from the world.

Most foreign embassies have closed, and the World Bank said this week it had suspended its operations in Yemen, citing security concerns.

In another sign of turmoil spreading on Thursday, three people were killed in a gunfight between militiamen loyal to Western-backed President Abd-Rabbu Mansour Hadi and a rival camp in the southern port city of Aden, where Hadi fled after escaping Houthi house arrest in Sanaa last month.

Elsewhere in the south, Houthis opened fire on hundreds of people protesting at their presence in the city of Al-Bayda on, killing one and wounding eight others, local officials and medical sources said.

Western and regional powers are particularly concerned about the security situation in Yemen because of its proximity to Saudi Arabia and the presence of one of al Qaeda's most active wings.

Saudi Arabia, which says the Houthis are controlled by rival Shi'ite power Iran and has attacked their forces before, did not comment on news of the military drill. Tehran denies any such support.

Qatari Foreign Minister Khaled Al-Attiya, speaking after a Gulf Cooperation Council (GCC) meeting in Riyadh, said the members of the organisation had "enough capability to protect its territories and sovereignty".

"A move here and there would not affect the GCC states," Attiya told a news conference.

The drill in the al-Buqa region in the Houthis' home province of Saada included heavy weapons acquired from the Yemeni army, local tribal and Houthi sources said.

"This is normal because Yemen is facing internal and external challenges. They (the exercises) are in preparation for any aggression," Houthi commander Mohammed Al-Bukheiti said.

Certain factions in the deeply divided Yemeni army have allied themselves with the Houthis against President Abd-Rabbu Mansour Hadi.

The president has tried to consolidate his control over Aden since he fled there.

Last week, he sacked the commander of the city's military garrison, a Special Forces contingent led by a general viewed as loyal to Hadi's predecessor, Ali Abdullah Saleh, who the United Nations says is ally of the Houthis.

General Abdel-Hafez Al-Saqqaf refused to step down, culminating in a gunfight on Thursday in which one soldier and two members of a local militia loyal to Hadi were killed, according to Aden residents. - Reuters