By Michelle Nichols

UNITED NATIONS (Reuters) - Yemen asked the United Nations Security Council on Tuesday to back military action by "willing countries" to combat an advance by Shi'ite Muslim Houthi militia, according to a letter from President Abd-Rabbu Mansour Hadi seen by Reuters.

Hadi wants the 15-member body to adopt a resolution to authorize "willing countries that wish to help Yemen to provide immediate support for the legitimate authority by all means and measures to protect Yemen and deter the Houthi aggression."

Hadi said he has asked the Arab League and the Gulf Cooperation Council comprised of Gulf Arab states "to provide immediately all means necessary, including military intervention, to protect Yemen and its people."

Violence has been spreading across the country on the Arabian peninsula since last year when Iran-backed Houthi militia seized the capital Sanaa and effectively removed Hadi, who seeks to return from the southern port city of Aden.

The United Nations warned on Sunday that Yemen's conflict could become an "Iraq-Libya-Syria" scenario if either side pushes for control. U.N. mediator Jamal Benomar said Yemen had been pushed "toward the edge of civil war."

Hadi cited Article 51 of the U.N. Charter, which covers an individual or collective right to self-defense against armed attack, as his legal justification for requesting military help from Arab countries.

"All our efforts for peaceful settlement have encountered absolute rejection by the Houthis who continue their aggression to subdue the rest of the regions out of their control," Hadi wrote. "There are military convoys destined to attack Aden and the rest of the south."

Forces loyal to Hadi drove Houthi fighters from two towns they had seized hours earlier on Tuesday, residents said. But other Houthi units entered the Red Sea port of al-Mukha overnight, leaving them a short drive from the Bab al-Mandeb strait, a sea lane vital to oil shipments.

The fighting in Yemen, a frontline in U.S. efforts to combat Islamist militants waging war across the region and beyond, has raised the prospect that regional rivals Iran and Saudi Arabia could be drawn into the conflict.

Yemen is home to Al Qaeda in the Arabian Peninsula, one of the global network's most active arms, which has carried out attacks abroad.

The U.N. Security Council condemned the takeover of much of Yemen and its institutions by the Houthis, urged them to withdraw, stated its support for Hadi and demanded an end to the hostilities in a statement adopted on Sunday.

The statement also threatened "to take further measures against any party" to the conflict in Yemen. In November, the council imposed sanctions on Yemen's former president, Ali Abdullah Saleh, and two Houthi leaders.

(Reporting by Michelle Nichols; Editing by Toni Reinhold and Alan Crosby)