A government statement on Sunday said: "A group of saboteurs led by Abdul-Malek al-Houthi carried out a rare attack yesterday (Saturday) on locations belonging to the armed forces and security in the province of Saada."
The statement did not say if there were casualties among the rebels.
Al Jazeera's correspondent in Sana'a, Murad Hashim, quoted local sources at the Yemeni northern province of Saada as saying that Yemeni military forces moved toward Safraa district on Sunday morning and deployed on top of a mountain.
They overlooked the main road linking Sana'a and Saada and leading to Al Samil district where a group of Yemeni Jewish families live.
"It seems that the presence of the troops annoyed a group of al-Houthi's supporters and ... clashes erupted that lasted for hours.
"Six security elements [troops] have been killed and another 20 injured according to a Yemeni official sources and one killed and five injured from al-Houthi's supporters, according to local sources in Saada which are unverified.
"Tension is still prevailing in the area yet the clashes have ended."
Cleric's followers released
In March, the Yemeni Security Supreme Committee announced the release of 627 followers of the cleric, following a pardon from the president, Ali Abdullah Saleh.
Yemen has accused the rebels of wanting to install Shia religious rule and of preaching violence against the United States.
Rebel supporters say the government is too closely allied with Washington and have accused authorities of seeking to silence the cleric's criticism of corruption.
The United States has provided military training to Yemen and assistance in border control.
Sunni Muslims make up most of Yemen's 19 million-strong population, while Shia Muslims account for about 15 per cent.