A statement from the Yemen's Supreme Security Committee said: "The state will strike these elements ... with an iron fist until they surrender themselves to justice."
Mohammed al-Qadhi, the foreign correspondent for Abu Dhabi's The National newspaper, said that hundreds had fled the fighting.
"They're launching an all-out war right now and we've heard reports from Sadaa that the military is using planes to attack the strongholds of the rebels and so many people are fleeing," he told Al Jazeera.
"The skirmishes and the clashes have been going on since last June, between the two sides.
"So many people have been fleeing to Sadaa town and this has put pressure on the camps of the refugees there."
The five-year-old battle between Yemen's Sunni-dominated government against the Shia Muslim Houthi fighters is one of a widening series of conflicts threatening to destabilise the country.
Yemen, one of the poorest Arab countries, is also combating a wave of al-Qaeda attacks and rising secessionist sentiment in the south.
Officials say the Houthi fighters, who belong to the Zaydi branch of Shia Islam, want to restore a form of clerical rule prevalent until the 1960s in Yemen when it was overthrown in a military coup.
A government committee criticised the fighters for not abiding by an agreement to end hostilities announced by Ali Abdullah al-Saleh, the Yemeni president, in July 2008.
In comments published in the press on Monday, al-Saleh blamed the fighters for the flare-up of violence in the north, saying he was "pained by attacks undermining security, repeated attacks targeting civilians, vandalism".
But Mohammed Abdel-Salam, a spokesman for the fighters, was reported by The Associated Press as saying that the group is only fighting for improved living conditions and wants the Yemeni army out.
"We will continue the fight until the army is withdrawn from the province," he was quoted as saying.
"We are only defending ourselves."
Over the past few weeks, local officials say the fighters have taken control of more of Saada province from government forces.
Last week, they seized an important army post near Saada's provincial capital on a strategic highway linking the capital Sana with Saudi Arabia after 12 hours of intense combat.
They have also taken control of several more towns.
Local officials said on Tuesday that the fighters seized key army posts near al-Malahidh crossing, about 20km south of the Saudi border.
The stability of Yemen is a crucial concern for both Saudi Arabia, which shares a border with Yemen, and the US.
Riyadh fears the conflict could make the kingdom's own Shia tribes directly across the border more restive.