Houthi fighters are gaining significant stretches of ground in Radaa, a district in al-Bayda governorate and a traditional stronghold of al-Qaeda in Yemen.
At least 50 Houthi fighters were killed in the latest clashes, Al Jazeera has learnt, but the armed group says it is now in control of Khobza, an area of Radaa previously held by al-Qaeda in the Arabian Peninsula (AQAP).
Al Jazeera's Hashem Ahelbarra, reporting from the capital Sanaa on Friday, said the battles were continuing, with al-Qaeda fighters calling for reinforcements.
"The Houthis say they will continue their fight until al-Qaeda is defeated or evicted from these areas," he said.
"They still have a strong presence in the capital, but they say when they see a strong military presence they will leave the city."
The rise of the Houthis has challenged the authority of President Abd-Rabbu Mansour Hadi, a Western ally and violence has continued despite UN-backed efforts to find a political solution.
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Instability in Yemen, which lies next to key shipping routes from the Suez Canal to the Gulf, arises from the 2012 overthrow of longtime President Ali Abdullah Saleh, who has been accused of backing the rebels.
Saleh is a member of the Zaidi sect, an offshoot of Shia Islam to which the Houthis belong.
Yemen's new cabinet was sworn in on Sunday after months of increasing instability in the country. The government is seen as a way to resolve Yemen's political crisis, despite the fact both Shia armed groups and Saleh called for an election boycott.
So far, the new cabinet has made no move to reactivate the army, which withdrew from the streets of Sanaa after the Houthis took over the city.
"It is going to take the government some time to redeploy the security forces," Al Jazeera's Ahelbarra said.
"Some weeks ago, when the Houthis swept into the capital, the army was sidelined, weakened and its reputation undermined.
"The top priority is the army and the police restoring security and leading the fight against al-Qaeda."
Source: Al Jazeera and agencies