Earlier on Sunday, Ali Abdullah Saleh, Yemen's president, called for a permanent end to fighting in the north, especially in Saada province, the Houthi's stronghold.
"Six wars are enough. Yes to security, stability and peace in Saada. No to the latest war," Saleh said.
"Stop jeopardising the security and stability of the province of Saada."
Saleh's call came after tribal mediators announced on Saturday that they had persuaded the Houthi rebels and the Bin Aziz tribe to stop firing.
The week's clashes had rattled an already fragile truce agreed in February that ended a six-month round of fighting between the rebels and the army, which began in 2004.
Mohammed Abdulsalam, a Houthi spokesman, told The National newspaperthat the rebels viewed the Bin Aziz tribe and Saleh's government as one and the same.
"We are not fighting tribes, [the government] just wanted to give a tribal dimension for the fight and this, of course, will not serve the country but would lead to catastrophe. Bin Aziz is a military leader and has military camps. It is the army which is shelling our people, using tanks and rockets," Abdulsalam said.
Saleh, who also faces a secessionist movement in the south and the presence of al-Qaeda in his country, has publicly pushed for a peace agreement with the Houthis.
The fighting took on regional dimensions late last year when it was reportedthat Saudi Arabian jets struck rebel camps inside Yemen after the rebels launched cross-border attacks.
The Houthis and the Yemeni army have continued to clash, each side blaming the other for violating ceasefires.