They said police as well as supporters of cleric Husain Badr al-Din al-Huthi were killed in the clash late on Wednesday, the latest in a series of clashes between security forces and rebels in Saada province, 240km north of the capital, Sanaa.
Fifty people were also wounded in Wednesday's firefight, which came after 15 state troops and 13 rebels were killed in ambushes and clashes on Monday and Tuesday.
The deputy head of Yemen's armed forces, General Ali Hamad Salah, told a government newspaper on Thursday that security forces were surrounding the area while local authorities and tribal elders tried to convince the rebels to surrender.
"They must hand themselves in to security forces and then they will stand trial," the weekly, September 26, quoted Salah as saying on its website.
Al-Huthi, a Zaidi Shia cleric, was
killed by Yemeni forces in 2004
Al-Huthi, a Zaidi Shia Muslim sect leader who founded a group called Believing Youth, was killed in September after two months of clashes with security forces in which 200 rebels and state troops died.
Yemen accused al-Huthi of forming an armed group that staged violent protests against the US and Israel.
Yemeni security sources have blamed al-Huthi's elderly father, Shaikh Badr al-Din, for the new round of violence.
They said he had shunned a government amnesty, quit Sanaa and returned to his Saada stronghold to foment violence.
Yemen joined the US-led "war on terrorism" after the 11 September 2001, attacks.
It has cracked down on al-Qaida-linked groups after attacks at home, including the 2000 USS Cole bombing and the 2002 attack on the French supertanker Limburg.