The rebels, known as Houthis, seized the capital Sanaa in September and have been advancing south alongside forces loyal to former President Ali Abdullah Saleh. In recent days they have closed in on the southern port city of Aden, where the internationally recognised President Abed Rabbo Mansour Hadi is now based.
Massive protests were held in the third largest city of Taiz -- which the rebels largely seized over the weekend -- and in Torba, some 60 miles (100 kilometres) away, where witnesses said the streets were filled with thick black smoke from burning tires and where protesters torched three armoured vehicles.
A medical official said six protesters were killed and dozens wounded in Torba. Local activists posted pictures on social media of what they said were dead protesters, their clothes drenched in blood.
Another witness, Mohammed Salem, said that Houthis and Saleh's forces fired anti-aircraft guns to scare off the protesters, "but the number of protesters increased instead."
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In a statement, Yemen's Socialist Party warned that the Houthis' invasion of the mostly Sunni south would set off a "sectarian war."
But Saleh never fully retired, and has been widely accused of acting through his loyalists in the government and security forces to derail the country's democratic transition. He is now allied with the rebels, and his loyalists helped the Houthis to take over the airport and other government buildings in Taiz.
In addition to dispersing the protesters, the Houthis also engaged in heavy fighting with militias loyal to Hadi in the city of al-Dhalea, where the two sides used artillery, anti-aircraft guns and machine guns, according to a Yemeni security official. The Houthis and troops loyal to Saleh have taken over the governor's office there.