"We suspended military operations but made six conditions, clearly stated. The first of which was demining, opening of the roads, lifting checkpoints and ceasing attacks on the armed forces.
"This was the first condition ... the Houthis did not respect these conditions. So the army has no choice but to continue its operations in self-defence."
Saleh said that the armed group was using its unilateral truce declarations to obtain ammunition, landmines, explosives and weapons from smugglers operating in the Arabian and Red seas.
"We know who they are. They claim to have a legitimate right to rule the country, and that the current government in power since the revolution 47 years ago is an usurpating power," he said.
"They claim that they have a divine right, and that they are the descendants of the Prophet. In fact, they are murders, rebels and outlaws ... we need to continue our mission in order to eradicate this malignant cancer."
Meanwhile, whole villages are fleeing a widening conflict that is creating a shameful and worsening emergency, aid workers say.
People in the area's main town, Saada, may be worse off still, trapped by shelling and streetfighting in homes with barely any water, power or communications and facing food prices spiralling out of reach - if they can make it to market.
"The situation is getting worse and worse and worse. We're not confronted with a humanitarian crisis, it's becoming a humanitarian tragedy," Gian Carlo Cirri, country director for the UN World Food Programme, said.
The UN is asking for $23.5 million extra to help Yemen but donor response so far "has been limited", Cirri said
UN agencies estimate the conflict has added another 50,000 people to 100,000 or so left homeless earlier by fighting in the poorest Arab nation. Most are women and children.
A month ago a new wave of fighting - the "sixth war" in an intermittent five-year-old conflict - erupted in the mountainous north between Zaidi Shia Muslims and government forces trying to impose central authority.