The sources say the clashes were triggered by an ambush of a senior security chief by al-Huthi loyalists on May 16.
Tarq Al Shami, head of media for Yemen's ruling party, said al-Huthi supporters were risking the collapse of a recent peace deal agreed in Qatar.
"All mediation efforts were foiled by al-Huthi supporters prompting the government to take decisive steps," he said.
"We are still receptive to mediation offers. We take mediation initiatives very seriously, but we do not and shall not tolerate terrorist activities.
"The state has to assume its responsibility and protect its citizens."
Al-Huthi's fighters are aiming to restore a Zaidi imamate in Yemen, which was overthrown by a 1962 republican coup.
An offshoot of Shia Islam, Zaidis form a minority in the mainly Sunni country but form the majority community in the far north of the country.
Ali Abdullah Saleh, Yemen's president, is a Zaidi, but the opposition fighters say that his government is illegitimate.
The two sides signed a peace deal in June last year, but there have been differences between them over the accord's implementation.
In February, Qatari mediators helped broker a new agreement which requires the government to release imprisoned al-Huthi loyalists, dismantle roadblocks and withdraw troops from urban areas of Saada in return for the opposition forces' disarmament.
Al-Huthi loyalists allege that Yemeni authorities have not observed the terms of the agreement but said they had launched new talks with the government earlier this month.