Troops sealed off villages in Saada province near the border with Saudi Arabia on the lookout for followers of anti-government cleric Shaikh Husain Badr al-din al-Huthi, who was killed by Yemeni armed forces last year.
Twenty-three fighters and 10 members of the army and security forces have been killed since the violence erupted early on Monday, tribal sources say, adding that another 51 fighters have been detained by the authorities.
There was no official confirmation of the casualties or the arrests.
Early on Tuesday, shots and artillery could be heard from the northwestern mountains where soldiers backed by tanks and armoured vehicles cordoned off villages and raided houses.
Fighters were suspected to be holed up in the mountains.
The clashes were the most serious confrontations between security forces and al-Huthi followers since his death in 2004.
Yemeni security forces said the renewed clashes were led by the preacher's father, Badr al-Din al-Huthi, after he "launched treacherous and cowardly attacks" on several security outposts in the province.
But tribal sources said the violence was sparked by an attempt by security forces to strip al-Huthi's followers of their heavy weapons. The authorities accused al-Huthi of seeking to foment sectarian strife, but he had said he was targeted because of his anti-US stance.