He also blamed the government for recent battles that left hundreds dead on both sides, saying the army's attacks on rebel-held villages amounted to "genocide".
Aid organisations have previously said that several Shia villages near Saada have been almost destroyed by heavy fighting and estimated that at least 5,000 people in the area have been forced from their homes.
Al-Houthi also said that the rebels, who are members of Yemen's minority Shia community, would continue their fight to topple the Yemeni government and replace it with a Shia theocracy.
"The ruling regime faced a big failure in defeating the sons of Saada," al-Houthi said, referring to the mainly Shia governorate in northern Yemen that has been at the centre of the revolt.
"We have the capabilities and the spirit to continue the war, launched against us by this unjust authority."
The rebels are defending heavily fortified villages in mountainous and remote parts of northern Yemen have so far held off the Yemeni army for nearly three years.
'No funding from abroad'
|The heaviest fighting occurs between Sanaa, the capital, and Yemen's northern border|
Al-Houthi also rejected reports that the rebels were receiving money and support from abroad.
"These are lies, we didn't receive any funds from outside," he said, accusing the Yemeni government of itself having foreign loyalties.
"It [the government] is the one that is loyal to America, and the one that is mobilising, attacking, destroying and slaying its own people, and shedding their blood for the sake of satisfying America."
Also on Saturday, several local officials in Saada and a doctor in the region, speaking on condition of anonymity, said that 1,500 government troops and 2,000 rebels had been killed in the fighting since the beginning of the year. They also said 2,800 soldiers had been wounded.
Government officials have said the deaths on both sides were in the hundreds.