Meanwhile witnesses said on Saturday that four soldiers also died.
Some 50 armed supporters of rebel preacher Husain Badr al-Din al-Huthi were also wounded when they attacked a military position north of the town of Saada with rocket-propelled grenades (RPGs) on Friday, the defence ministry's web site said.
Military sources said one soldier was killed and five wounded, but witnesses put the toll at four dead and four wounded.
Dozens of the preacher's supporters were also captured on Friday in assaults on rebel positions in al-Shafa and al-Ruzmut, and on the village of al-Hamzat northeast of Saada.
Witnesses said the army had met fierce resistance.
Nearly 200 people have now been killed in the clashes which broke out on 18 June.
Yemen is offering $55,000 reward
for the capture of al-Huthi
The army has been steadily closing in on al-Huthi's strongholds in the rugged Maran district close to the Saudi border.
The authorities have offered a 10 million riyals ($55,000) reward for information leading to the capture of the preacher, whom they accuse of seeking to foment sectarian strife.
The Zaidis are a Shia Muslim sect dominant in north-western Yemen but in the minority in the mainly Sunni country.
Troops and police stepped up their offensive against the self-styled "Amir al-Muminin", or Prince of Believers, after the abandonment of a mediation effort by MPs and other dignitaries on 28 June.
Earlier this week, President Ali Abd Allah Salih, who has accused foreign elements of supporting Huthi's uprising, called on the preacher to turn himself in, promising him a fair trial.
Al-Huthi, who was himself an MP from 1993 to 1997, enjoys the support of up to 3,000 armed rebels, according to activists close to the preacher.
According to Salih, the Zaidi preacher heads the "Faithful Youth" organisation, formed in 1997 as a breakaway from the Islamist opposition movement al-Haq.