The Zaidis are an offshoot of Shia Islam dominant in northwestern Yemen, but form a minority in the mainly Sunni country.
Sanaa said in April 2005 it had crushed the Zaidi "Young Believers" uprising led by Badreddin al-Huthi after his son Hussein was killed by government forces the previous September.
The ruling General People's Congress (GPC) of Ali Abdullah Saleh, the Yemeni president, said on its website on Wednesday that five soldiers, including an officer, were killed in "terrorist attacks led by members of the (rebel) group".
Zaidi fighters are also suspected of being behind attacks on Saturday and Sunday against army and police which left seven soldiers dead and 20 others wounded.
|Hundreds of al-Huthi's supporters are on|
trial for alleged terrorist attacks [EPA]
On Monday Saleh called on the fighters to lay down their arms and surrender.
"Those saboteurs and terrorists who belong to [tribal Zaidi leader] Abdul Malek al-Huthi should hand in their heavy and medium weaponry to the [army] command in the Saada region," he said in an address to military commanders.
There has been no official indication of Zaidi losses, but the security source told AFP on Thursday said that "three rebels were killed on Wednesday at a village in Saada province".
The Huthi tribe led an armed campaign against government forces in 2004 and 2005 that left around 700 dead and hundreds more wounded.
Since then there have been intermittent outbreaks of fighting.
Al-Huthi's supporters reject as illegitimate the government which seized power in a 1962 coup known as the September 26 revolution, overthrowing a Zaidi imamate.