The two soldiers were killed on Monday evening when suspected supporters of the Zaidi preacher Husain Badr al-Din al-Huthi attacked a military site near Saada, about 250km north of the capital Sanaa, local sources said on Tuesday.
They said more than 10 other soldiers were wounded in the attack. A website run by the Islamic-oriented opposition party (Islah) said five of al-Huthi's supporters were killed last night when military gunships fired missiles at a local marketplace in the Marran area, where he was hiding.
The defence ministry said that a close aide of al-Huthi, identified as Zaid bin Ali al-Huthi was killed by security forces
surrounding the cleric and scores of his armed followers.
The man was killed in a raid on a house belonging to the religious leader in the besieged area of Marran, the ministry said in a statement.
Although the statement said that the government forces succeeded in inflicting losses on followers of al-Huthi, details on casualties were not available.
Sixty-eight followers of the cleric have been reported arrested
since clashes erupted on 21 June. Yemeni authorities accuse al-Huthi of organising protests against the United States and Israel in mosques in Saada and the capital Sanaa.
The central government deployed hundreds of troops last week in Marran and launched a massive chase for al-Huthi, a former MP and a leader of the Shia sect.
Two soldiers were killed in clashes
with al-Huthi's supporters
Al-Huthi is also accused of receiving foreign financial aid aiming at disturbing the country's security and stability, according to an Interior Ministry statement last week.
In its weekly meeting on Tuesday, the Cabinet listened to a report by the interior ministry about the ongoing operation and hailed the measures taken to deal with those elements who disturb the security and violate law and constitution, according to the official Saba news agency.
The council also instructed the government forces to strictly deal with those elements and quickly crush this strife which is "an act of terrorism", the agency reported.
One security official said on Monday that the operation was expected to be brought to an end soon, with government forces tightening their grip on the cleric's whereabouts.
Yemen is a close US ally in the Arab world and the impoverished country has cooperated with the United States in chasing suspected members of the al-Qaida network.