By Mohammed Mukhashef
ADEN, Yemen (Reuters) - Forces loyal to Yemeni President Abd-Rabbu Mansour Hadi drove Houthi fighters from two towns they had seized hours earlier on Tuesday, residents said, apparently checking an advance by the Shi'ite fighters towards his refuge in Aden.
But other Houthi units overnight entered the Red Sea port of al-Mukha, security officials and residents said, placing the Iranian-backed fighters a short drive from the Bab al-Mandeb strait, a sealane vital to oil shipments.
And in Taiz, soldiers and Houthi gunmen shot dead at least four people as demonstrators took to the streets to protest against the Houthi take-over of the central highland city, medical officials and witnesses said.
Fighting has spread across Yemen since last September when the Houthis seized the capital Sanaa and advanced into Sunni Muslim areas, raising the prospect that regional rivals Iran and Saudi Arabia could be sucked into the conflict.
Hadi, a former general seen by the Shi'ite Muslim Houthis as a pawn of Sunni Gulf Arab monarchies and the West, has been holed up in Aden since he fled Sanaa in February.
His forces have stationed tanks and artillery on a number of roads linking north and south Yemen. An array of tribesmen, militiamen and army units loyal to him are resisting the southward advance of the Houthis.
Skirmishes have escalated since the weekend and Tuesday's fighting showed the fluidity of the military contest.
The northern-based Houthis had seized Kirsh, a town about 100 km (62 miles) north of Hadi's base in the southern port of Aden. But army units, tribesmen and militiamen pounded the fighters with rockets and heavy artillery, forcing them to withdraw northwards, military officials and residents said.
Hadi's forces also counter-attacked in Dhalea town, reversing the Houthis' first inroads into the territory of the formerly independent south. The town has for years been the center of an armed movement to secede from the Yemeni capital Sanaa.
A Houthi official expressed continued mistrust of Hadi, saying he had allied himself with Islamist militant forces. But but added the Houthi forces had no designs on Aden or any other region. Hadi has a strong record as an opponent of al Qaeda.
"We are not targeting Aden, the South or any other region, just takfiri groups that are in some areas allied with various political forces," Houthi official Mohammed al-Bukhaiti said by telephone, using a derogatory term for hardline Sunni Islamists who accuse Shi'ites and others of being infidels.
"What is going on now we consider self-defense and the defense of our society."
Bukhaiti also said the movement saw no reason to move peace talks from Yemen to Qatar but it had not definitively rejected the idea. A Qatari foreign ministry source said earlier Doha would host talks between Yemen's factions.
The rise of the Houthis has opened a new chapter of instability in Yemen, a perennially turbulent neighbor of oil power Saudi Arabia and a frontline in U.S. efforts to combat Islamist militants waging war across the region and beyond.
Their entry into al-Mukha took them to within 80 km (50 miles) north of Bab al-Mandeb strait, which links the Mediterranean Sea and Indian Ocean via the Suez Canal and Red Sea. More than 3.4 million barrels of oil per day passed through Bab el-Mandeb in tankers in 2013, according to the U.S. Energy Information Administration.
The U.S. ambassador to Yemen, speaking in Washington on Monday, said he believed a political power-sharing agreement between the rival factions was still possible but the United States and its allies need to make decisions quickly.
"Political dialogue won't work if Hadi is overrun and captured, and Aden falls, which could happen very quickly,"
Ambassador Matthew Tueller told Reuters.
Tueller said Saudi Arabia had offered to host peace talks among the warring Yemeni factions on April 7, but that date was still three weeks away and the situation was eroding quickly.
The United States on Saturday evacuated its remaining personnel from Yemen, including about 100 special operations personnel, because of deteriorating security.
Yemeni Foreign Minister Riyadh Yaseen appealed on Monday for Gulf Arab military intervention to halt the Houthi advances.
Saudi Foreign Minister Saud al-Faisal said the Gulf Arab states would take steps to back Hadi and he accused Iran of trying to sow sectarian strife in the region.
((For graphic, click on http://link.reuters.com/jeh44w ))
(Reporting By Mohammed Mukhashaf and Mohammed Ghobari,; Writing by Noah Browning, Editing by William Maclean and Angus MacSwan)