The fighters said on their website that they killed another eight soldiers in clashes on Friday in Saada town.
A military source confirmed that the Houthis had launched an offensive against the town from the suburbs, but said it had been repulsed and that several attackers had been killed.
The Houthis also attacked the home of Othman Mujalli, a leading trial chief in Saada province who is a member of the Yemeni parliament and recently rallied to the government's defence, provincial officials said.
Mortar fire killed Mujalli's son, Hamid, and four other civilians, they said.
The clashes came as truce offers between the two sides faltered over continued military action by Saudi government forces which intervened in the fighting late last year.
In another related development, the brother of the Houthis' leader was sentenced in absentia to 15 years in jail on Saturday.
Yahya al-Houthi, a parliamentarian who has been based in Germany since leaving Yemen three years ago, is the brother of Abdul-Malik al-Houthi, the military leader of the Houthis.
At the end of a trial which began in October, Yahya al-Houthi was convicted of supporting the armed campaign.
The conflict with the northern Houthis, who complain of social, religious and economic discrimination, started in 2004, but intensified last year.
Yemen also faces a secessionist movement in the south and a resurgent al-Qaeda.