Army forces launched a fresh offensive late on Tuesday on the mountainous Maran district of Saada province where Husain Badr al-Din al-Huthi and thousands of his supporters are besieged, the sources said on Thursday.
The dead and wounded were on both sides, they added.
A military source, who did not wish to be identified, said a large number of al-Huthi's followers had surrendered to the advancing army.
Witnesses said the army crossed the al-Sharaf mountain before advancing half-way across al-Hikmi mountain, the highest peak in the Maran area and a key stronghold of al-Huthi and his followers.
The military sources said the army expected an early end to the fighting after the advances made by the army in the new offensive.
Al-Huthi was a former MP from
the Zaidi community
The onslaught came after the failure of new efforts by mediators from the opposition, tribes and clergy to negotiate the surrender of al-Huthi and his followers, the sources added.
The clashes between the army and al-Huthi's supporters, estimated to number as many as 3000, have left at least 340 people dead since 18 June but the full toll could be higher as the army has given few details of its own casualties.
Authorities have offered a 10-million-riyal ($55,000) reward for information leading to al-Huthi's capture.
Al-Huthi, a preacher and former MP from the Zaidi Shia Muslim community, heads the Faithful Youth organisation, an offshoot of the Islamist opposition movement Al-Haq.