The Shiite Huthi militia, backed by troops allied to former president Ali Abdullah Saleh, clashed with armed tribesmen in Baida province late Monday, the sources said, adding that nine tribesmen and 15 Huthi fighters were killed.
The tribesmen booby-trapped two houses used as bases by Huthi fighters and ambushed several patrols, the sources added.
Meanwhile, clashes raged late Monday in Marib, east of Sanaa, where tribesmen loyal to Yemen's internationally backed President Abedrabbo Mansour Hadi confronted advancing Huthi fighters and pro-Saleh troops, tribal sources said.
The advancing forces included units from the former presidential guard, an elite force that Saleh built during his three-decade rule, the sources added.
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The gunfights took place as the Huthis, who seized control of Sanaa last year, sent additional reinforcements south, upping pressure on Hadi, who is refuged in the southern port city of Aden.
Hadi last month escaped house arrest in Sanaa imposed by the Shiite militia, fleeing to Aden where he retracted an earlier resignation tendered under pressure from the Huthis.
Although Saleh resigned in 2012 following nationwide protests, he has continued to enjoy widespread support from the armed forces, and is accused of aiding the Huthis in their advance south from their northern mountain stronghold.
Military sources in south Yemen said that reinforcements from the army's Al-Hamza Brigade -- under Saleh's command -- had been mobilised from central Ibb province to Qatabah, in Daleh, some 120 kilometres (75 miles) north of Aden.
The reinforcements came as anti-Hadi forces deployed south of the key city of Taez, which lies strategically on the road between Sanaa and Aden.
Demonstrations continued Tuesday in Taez against the arrival of pro-Saleh forces and militiamen in the city, after security sources said they seized the airport.
The head of Taez police denied late Monday that the airport or other government installations had been taken over.
In a statement carried by Saba state news agency, which is now controlled by anti-Hadi forces, General Mutahar al-Shuaybi said air traffic at Taez remained "normal".