Yemen's Iran-aligned Houthi group broadcast footage on Sunday that it said showed a major attack near the border with Saudi Arabia's southern region of Najran, adding that its forces had captured troops and vehicles.
Saudi Arabia, which leads a coalition that has been battling the Houthis, has not responded to Saturday's Houthi announcement that they had carried out the attack.
Reuters could not independently verify either claim.
Houthi-run al-Masirah TV broadcast images of armored vehicles hit by blasts and what the Houthis said were dozens of surrendering fighters. Two of those men, speaking to the camera, said they were from Saudi Arabia.
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The Houthi military spokesman said the offensive 72 hours earlier had defeated three "enemy military brigades", leading to the capture of "thousands" of enemy troops, including Saudi army officers and soldiers, and hundreds of armored vehicles.
The spokesman, Yahya Saria, did not give a day for when the footage was filmed.
Yemeni government troops, supported by air strikes of the Saudi-led coalition, have in recent months fought Houthi forces in the Kataf region of Yemen's northern Saada province near the Saudi border. Local sources have said the Houthis have captured scores of Yemeni troops in the battles.
The Sunni Muslim coalition, which receives arms and intelligence from Western countries, intervened in Yemen in March 2015 after the Houthis ousted the internationally recognized government from power in the capital Sanaa in 2014.
A UN-brokered prisoner swap deal agreed between the Houthis and Yemen's Saudi-backed government last December involving some 7,000 detainees on each side has yet to happen.
The Houthis, who had recently stepped up missile and drone attacks on Saudi cities, have claimed responsibility for the largest-ever attack on Saudi oil facilities on September 14.
Riyadh dismissed the claim, saying the assault did not come from Yemen and have Shi'ite Muslim Iran. Tehran denies this.
The Houthis said on September 20 they would halt missile and drone attacks on Saudi Arabia if the alliance stopped its operations. The coalition has not responded to the proposal.