The violence came as President Ali Abdullah Saleh charged that the rebels, followers of a slain cleric, were not abiding by the terms of an amnesty.
A police official said at least six rebels were killed late on Tuesday and another 10 on Wednesday around the Jabal al-Nusf area in Saada.
More than 500 soldiers and policemen, using tanks and armoured vehicles, sealed off parts of Saada and prevented journalists from entering, an AFP correspondent reported.
The renewed fighting between government forces and followers of slain Zaidi leader Hussain Badr Eddin al-Huthi comes after rebels killed eight policemen in Saada on Monday, tribal sources said.
Saleh accused the rebels of not respecting the terms of a September pardon after Huthi's death at the hands of the army and nearly three months of deadly fighting last year.
A total of about 680 people were killed in last year's fighting and in a two-week-long revolt in April of this year.
"Some of those who agreed to abide by terms of the amnesty and to stop repeating slogans that turn foreign countries into the enemies of Yemen were released from prison," Saleh said late on Tuesday.
Troops have sealed off parts of
the Saada province
"But the ones who did not abide by the rules were not released."
Saleh also promised the exiled Zaidi former ruling family compensation as part of the amnesty package.
The Zaidis are a Shia Muslim sect dominant in the far north of Yemen, but a minority in the mainly Sunni country.
The rebels reportedly want to re-establish the Zaidi imamate, which ruled northern Yemen until it was overthrown by republican officers in 1962.
One of Huthi's grandsons said the government was to blame for the fresh fighting after shoppers were attacked by security forces in a market in the town of al-Khafji in Saada.
"Your amnesty is not being implemented on the ground," Abdulmalik al-Huthi said in a letter to Saleh, a copy of which was obtained by AFP.
Zaidi leader Hussain al-Huthi was
killed by Yemeni forces last year
But tribal leaders, speaking on condition of anonymity out of fear of reprisals from both sides, said many of the 400 rebels released since September had retaken arms and rejoined the fight.
On Monday, Huthi's followers distributed leaflets in Saada reading: "Death to America, death to Israel, damn the Jews and glory to Islam."
In late August, prosecutors accused a group of Zaidi rebels of planning to strike the US embassy and assassinate the ambassador in a rocket attack.
Yemen is one of the world's poorest countries, with dwindling oil reserves.
It has been cracking down on suspected al-Qaida members since the 11 September 2001 attacks on the United States, a campaign it has conducted with the help of Washington.