Militants loyal to Yemen's exiled government ride atop a tank they seized from Houthi militiamen in the country's central city of Taiz on Monday. (Reuters)

Even as the Saudi-led invasion of Yemen has started to make rapid gains against rebel forces, lawlessness is plaguing newly liberated areas, and al-Qaeda militants are moving in to take advantage of the power vacuum, Yemeni residents and fighters say.

Factions within the coalition organized by the Saudis also have been turning against one another, sometimes with gunfire, as they pursue starkly different visions of Yemen’s future.

The Houthi rebels have been driven from large swaths of southern Yemen over the past several weeks, but little thought appears to have been given to securing the new areas.

The Saudis and their immediate allies are fighting to return President Abed Rabbo Mansour Hadi’s exiled government to power. Other militias, also arrayed against the Houthis, seek the secession of southern Yemen instead, and reject Hadi. And militants with Yemen’s powerful al-Qaeda affiliate — al-Qaeda in the Arabian Peninsula (AQAP) — are trying to reestablish a foothold they lost in 2012.

Analysts say that the radical group intends to eventually use captured territory to stage attacks against the West. The Saudi coalition does not appear to have attacked AQAP.

The situation is poised to worsen a humanitarian crisis that U.N. officials say threatens Yemen’s 25 million residents with famine.

“In Aden and the other areas, the security situation is messy,” said Wahid Ali Sallam, a militia leader in Aden. His fighters helped the coalition seize the key southern port city last month.

It is unclear whether the coalition intends to push north to the capital, Sanaa. Such an advance would trigger a tough response from the Houthis, who control Sanaa and have many supporters in the city and surrounding areas. But even if the plan is to first strengthen a pro-Hadi foothold in the south, this appears to have been complicated by the chaotic conditions in those areas, said Katherine Zimmerman, a Yemen expert at the American Enterprise Institute.

“It quickly became apparent that there wasn’t much of a plan to fill the vacuum after the Houthis were driven out,” she said.

Still, the battlefield victories are undeniable. The arrival of thousands of coalition troops in Yemen in recent weeks has turned the tide of a war that Saudi Arabia initially launched in March as an air offensive. Since then, more than 4,000 people have been killed and more than 1 million displaced.

The air bombardments appeared to have little effect on the Houthis, whom Saudi officials view as proxies for Shiite Iran. The Houthis, who overthrew Hadi’s government in February, deny that they are tools of any foreign power. Hadi and his cabinet now operate from Saudi Arabia.

As many as 3,000 troops from the United Arab Emirates have landed in southern Yemen in recent weeks, linking up with anti-Houthi forces, according to U.S. officials, fighters in southern Yemen and Houthi rebels. A smaller contingent, of Saudi soldiers and Saudi-trained Yemeni fighters, also is participating in the battles. Using tanks, armored-personnel carriers and assault helicopters, they are driving the rebels out of several provinces.

But after rebel fighters were pushed out of Abyan this month, AQAP militants took over government buildings and established checkpoints in the southern province’s capital, Zinjibar, according to local residents and fighters in the area.

AQAP militants already have seized areas in nearby Hadramaut, even though that province was not involved in the rebel attacks.

Brig. Gen. Ahmad Asseri, a spokesman for the coalition, confirmed the AQAP advances in Abyan. But the coalition’s emphasis is on fighting the Houthis at the moment, he said.

“We have to drive these Houthi militias out of the cities, and we have to help the legitimate Yemeni government restore order so that groups like al-Qaeda do not exploit the situation,” Asseri said.

In 2011, AQAP-linked militants declared an Islamic emirate in Abyan — where the group enjoyed support from the local population — before Yemen’s U.S.-backed military drove them out. Dislodging the group will be far more difficult now because Yemen’s military has disintegrated during the conflict, said Adam Baron, a Yemen analyst and visiting fellow at the European Council on Foreign Relations.

Within coalition ranks, tensions have erupted into full-blown clashes. In Aden last week, a military unit loyal to Hadi’s government attempted to take control of the presidential palace from a local militia.

The militiamen responded with gunfire before surrounding the soldiers and forcing them to withdraw from the palace, said Wahid Ali Sallam, the militia leader in Aden whose fighters were involved in the incident. The clash followed protests by the local militiamen over a lack of medical services for wounded fighters from Aden, he said.

Those protests included checkpoints that prevented the movement of officials and soldiers affiliated with the exiled Yemeni government. “We are willing and ready to go back out to the streets again, and we will push until our demands are met,” said Sallam.

Just to the north of Aden, in the Lahij province, southern separatists are calling for independence from the north now that Houthi forces in the area have been defeated. They fly the flags of the formerly independent state of South Yemen, which united with the north in 1990. Across much of the newly liberated territory, those flags — not the flag of united Yemen — are an almost-ubiquitous sight on government buildings and captured military facilities.

“We are not concerned with Hadi, his government or whatever the Saudis want. Our demand is clear: We want separation from the north,” said Awwad Ahmed al-Shillin, a militia leader.

Naylor reported from Beirut. Missy Ryan in Washington contributed to this report.