Houthi spokesman Yahya Sarea says the three-day "large-scale" operation was launched on August 25 and showed footage purportedly of the attack, but it was not clear why the announcement was being made weeks later.
Yemen's Iran-backed Houthi rebels said on Sunday they had killed some 200 pro-government fighters and took 2,000 others prisoner in an August offensive near the southern Saudi region of Najran.
The Houthi military spokesman, Yahya Sarea, said the offensive 72 hours earlier had defeated three "enemy military brigades," leading to the capture of "thousands" of enemy troops, including the Saudi army officers and soldiers, and hundreds of armoured vehicles.
"More than 200 were killed in dozens of (missile and drone) strikes while trying to escape or surrender," he said.
"Over 2,000 fighters were taken prisoner," he added, saying most of them were Yemeni but that they included other prisoners.
On Saturday, the Houthis had said that officers from Saudi Arabia –– which leads a military coalition against the rebels –– were among the captives, but those claims were not repeated in Sunday's televised press conference.
The footage showed a major attack near the border with Saudi Arabia's southern region of Najran, adding that rebels have captured troops and vehicles.
Saudi Arabia, which leads a coalition that has been battling the Houthis has not responded to Houthi announcement that they had carried out the attack.
Reuters could not independently verify either claim.
Two captured men say they're Saudis
Houthi-run Al Masirah TV broadcast images of armoured 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.
A Yemeni government source confirmed to AFP news agency that some 200 soldiers were killed in an attack in late August, but that only about 1,300 fighters were still being held, including 280 who were wounded.
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.
Prisoner swap deal
The Sunni Muslim coalition, which receives arms and intelligence from Western countries intervened in Yemen in March 2015 after the Houthis ousted the internationally-recognised 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.
Saudi oil attacks
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 Shia 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 Sauid-led coalition has not responded to the proposal.