Yemen rebels say made gains in central Al-Bayda province
Operations have led to "the liberation of the Naman and Nateh districts" in Al-Bayda, Houthi spokesman Yahya Saree said in a statement carried by the rebels' Al-Masirah television.
The Houthis are in the "process of clearing out the remaining pockets in Al-Bayda province after liberating most areas", he added.
The announcement comes after the country's warring sides deployed reinforcements to the nearby district of Bayhan earlier this week.
The possible fall to the rebels of Bayhan, located in Shabwa province and strategically near the border with Marib, could pose a major threat to the government.
A government military source told AFP on Monday that fighters from both sides were dispatched to the outskirts of Bayhan after the Houthis seized Nateh and Naman.
Al-Bayda's deputy governor told AFP that the insurgents had taken control of the two districts, displacing many civilians.
The Houthis in February escalated their efforts to seize Marib, the government's last northern stronghold, and the fighting has killed hundreds on both sides.
Control of the oil-rich region would strengthen the Houthis' bargaining position in peace talks.
The battle has also raised fears of a humanitarian catastrophe, as many Yemenis had fled to the area to escape fighting in other parts of the country.
Yemen's conflict flared in 2014 when the Houthis seized the capital Sanaa, prompting Saudi-led intervention to prop up the internationally recognised government the following year.
While the UN and Washington are pushing for an end to the war, the Houthis have demanded the re-opening of Sanaa airport, closed under a Saudi blockade since 2016, before any ceasefire or negotiations.
The fighting has killed tens of thousands and left some 80 percent of Yemenis dependent on aid, in what the UN calls the world's worst humanitarian crisis.