SANA, Yemen — More than three weeks after Saudi Arabia began a bombing campaign aimed at crippling his movement, the leader of Yemen’s Houthi rebels responded with defiance on Sunday in a televised speech, saying that Saudi attempts to “humiliate” his country were doomed.

“Those who want the people to give in are just dreaming,” the leader, Abdel-Malik al-Houthi, said in a long, fuming address that was also sharply critical of the United States. “Our Yemeni people have the right to fend off the aggression, and to confront the aggressor with all possible and available means,” he said on a Houthi news channel.

Mr. Houthi gave no indication that he was willing to negotiate with the Saudis or to agree to their conditions for a cease-fire, including that the Houthis withdraw from cities they have captured. His defiance suggested a prolonged war and raised further questions about the Saudi government’s military strategy, which has been centered on pounding the Houthis and their allies from the air.