Its official website said on Tuesday that security forces arrested more than 30 supporters of Hussain Badr al-Din al-Huthi who were involved in the fighting, which began late on Sunday.
"Security forces continue to encircle the rest of elements hiding in the Hidane region", in Saada province, about 250km north of Sanaa.
Tribal sources said earlier that security forces were attempting to force the remaining fighters to surrender.
They said the army used heavy weapons in the fighting, during which there were also an undetermined number of civilian casualties.
The army laid siege to hundreds of Huthi's supporters on Monday. Armed partisans also came out in force in two other locations in Saada, the sources said.
Yemeni authorities accuse Huthi of stirring up trouble by organising anti-US demonstrations after weekly Muslim prayers on Fridays.
His supporters are "outlaws ... extremists and trouble-makers", the Defence Ministry said, adding that they would be brought to justice.
"They have opened fire on government institutions, police
pickets and roughed up students to stop them from going to school," it added.
Yemen has cracked down on suspected al-Qaida members and other Islamist fighters since the 11 September 2001 attacks in the United States and a series of clashes at home.