Houthi militants took over the airport in Taiz as they swept through the city and surrounding province, two officials with the Taiz provincial government said.
One civilian was killed and 82 others wounded when the rebels fired at local residents protesting their presence, the officials said.
The rebels have also seized security and intelligence buildings in Taiz and set up checkpoints in the area, the officials said. Taiz, about 390 kilometers (240 miles) south of Sanaa, is Yemen's cultural capital.
The rebels -- Shiite Muslims who have long felt marginalized in the majority Sunni country -- surrounded the presidential palace
in January. Yemen's President and his Cabinet resigned
Ousted President Abdu Rabu Mansour Hadi says his resignation wasn't valid and maintains that he remains the country's leader.
In a statement Sunday, the United Nations Security Council backed Hadi, calling for all sides to end armed hostilities and work out differences at the negotiating table.
"Peaceful dialogue is the only way forward," said Jamal Benomar, the U.N.'s special adviser on Yemen.
But he gave a dire assessment of the current situation, saying the country is in a "rapid downward spiral" and at "the edge of civil war."
This isn't the first time the U.N. Security Council has weighed in on the mounting tensions. Last month the council slammed the rebels
for taking over democratic institutions and holding officials under house arrest.
But so far, it seems calls for calm from around the world have done little to quell the violence.
Last week, a Yemeni jet commanded by the Houthi fired missiles at a palace housing Hadi in the port city of Aden. No one was injured, but the direct strike marked an escalation in the deadly fighting between the two sides. That same day, Yemeni military forces -- some under the Houthis, others led by officers loyal to Hadi -- battled in Aden, leaving at least 13 people dead in the clashes, Aden Gov. AbdulAziz Hobtour said.
Bombings at two mosques in Sanaa last week killed at least 137 people and wounded hundreds more. ISIS claimed responsibility in a statement posted on a site that has published previous statements from the group.
On Saturday the State Department said the U.S. military had pulled its remaining personnel out of Yemen
due to the deteriorating security situation.