In the past three weeks, the campaign "has been able to degrade and destroy much of the military infrastructure that Huthis and (former president Ali Abdullah) Saleh possess," said ambassador Adel al-Jubeir.
He told reporters in Washington that "we are also beginning to see cracks" in the Huthi and Saleh military ranks and "we see military commanders defecting back to the regular Yemeni military."
"We expect to see more and more of them as pressure intensifies," he said, adding "this operation will continue until objectives are achieved. There can be no half measures."
The Shiite rebels then advanced on the main southern city of Aden, where President Abedrabbo Mansour Hadi had taken refuge, forcing him to flee to Riyadh.
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The Huthis have allied with troops loyal to Saleh, who was forced from power in 2012 following a year of nationwide protests against his three-decade rule.
But Jubeir said deliveries of arms to the Huthis from Iran appeared to have stopped since the start of the intensive air strikes.
And he also demanded that Iran stop interfering in Yemen, saying the two countries did not share a border.
"There is no reason for Iran to be involved with Yemen. There is no reason for Iran to be supporting one faction against the other," Jubeir said.
"The Iranians should be supporting all Yemenis. That's how we bring about stability and security and safety."
Local Yemeni defense committees backed by Saudi Arabia were also beginning to have success, and had managed to wrest back a large part of Aden as well as other parts of the country.
Earlier, Egypt said it was considering holding "large-scale" military exercises with Saudi Arabia in a possible sign the air campaign may expand into a ground operation.