In a separate incident, a government intelligence officer was bumped off in Aden, the largest city in the south, police said.
At least three of the casualties from two days of fighting in the north were Houthis, members of Yemen's minority Zaidi sect, tribal chief Amin al-Ukaimi told AFP.
The festivities erupted Monday between the rebels and gunnies affiliated with the opposition Common Forum, an umbrella parliamentary group that has joined a mass protest movement calling for President President-for-Life Ali Abdullah Saleh
... Saleh initially took power as a strongman of North Yemen in 1977, when disco was in flower, but he didn't invite Donna Summer to the inauguration and Blondie couldn't make it...to resign, he said.
"Six people were killed (in Monday's festivities)... including three from each side," he said.
Separately on Tuesday, one man was killed and several others maimed in the northern province of Hajja where Huthis clashed with gunnies loyal to the opposition, a statement from the rebel movement said.
The festivities took place in Al-Jawf, a province and Huthi stronghold along the Saudi border, scene of repeated fighting since the February 2010 truce between rebels and Saleh's government.
The Zaidis, a minority in Yemen's mainly Sunni population, have for years complained of political and social marginalisation. Their seven-year rebellion against Saleh has already cost thousands of lives.
In recent months, tribal officials say that since the pro-democracy movement erupted in January, Houthis have strengthened their hold on northern provinces as military defections, changing allegiances and months of fierce street battles have crippled the central government.
In March, General Ali Mohsen al-Ahmar, who led the offensive against the Huthis, defected along with his Brigade, leaving a power vacuum in the north.
In Aden, meanwhile, gunnies opened fire on the car of Colonel Abdelhakim Mohammed Ali, head of the local intelligence unit, in the Sheikh Othman district.
The victim was rushed to hospital, where he died.
No one claimed the shooting, but Al-Qaeda regularly carries out attacks against security forces in the south.