“To avoid more bloodshed and to stop aggression on civilians … we offer this initiative,” al-Houthi said in an audio message.
A Saudi general had said earlier on Wednesday that the Houthi’s truce prompted the end of the fighting.
Yemen rebels ‘leave’ Saudi Arabia
Video: Hunger stalks Yemen’s displaced
Video: Saudis tighten Yemen border control
Video: Iran warns against Yemen meddling
Video: Saudi worried over Houthi fighters
Profile: Yemen’s Houthi fighters
Inside Story: Yemen’s future
“Last night, since they announced a ceasefire, they did not fire and we did not have any engagement,” Major General Said al-Ghamdi, commanding general of first paratrooper brigade, told journalists in the border area.
“They are not in our lands,” Ghamdi said. “The battle has ended by God’s will.”
But Khaled bin Sultan told a press briefing on Wednesday: “They did not withdraw. They have been forced out.”
Hashem Ahelbarra, Al Jazeera’s correspondent in Sanaa, said: “Forty-eight hours after the Houthi leader offered Saudi Arabia a ceasefire, the kingdom is responding with a carefully crafted statement.
“It doesn’t talk of a ceasefire, instead it claims they have achieved their military goals and therefore managed to defeat the Houthi fighters.”
“They don’t want to give any mixed signals to the Saudi people, that they are giving concessions to the Houthi rebels.”
The border has been the scene of on-off fighting between Yemeni Houthi fighters and Saudi troops since early November.
Al-Houthi vowed to wage an “open war” against Saudi Arabia if they ignored the ceasefire offer and continued attacks against his group’s positions.
“Its [Saudi Arabia] insistence to continue the aggression after this initiative gives us the legitimacy to open new fronts and to wage an open war,” he said.
The so-called Houthi fighters seized an area of Saudi territory in November last year, drawing the kingdom into its long-running conflict with government forces.
The Houthis, who launched a rebellion against the Yemeni government in 2004, belong to the minority Zaidi sect of Shia Islam and complain of social, economic and religious marginalisation.
|Houthi fighters ventured into Saudi territory in November and confronted Saudi troops [AFP]|
Government forces launched “Operation Scorched Earth” on August 11 in an attempt to crush the rebels in the mountainous northern region.
Al-Houthi’s announcement on Monday came just three days after he appeared in a video recording denying claims by the Yemeni government that he had been injured or killed.
The rebel leader spoke briefly in the 35-second video posted on the group’s website showing him sitting on a chair with no visible injuries.
Saudi Arabia fears that the growing instability in neighbouring Yemen could turn into a major security threat for the kingdom.
The government in Sanaa is battling a secessionist movement in the south and a group calling itself al-Qaeda in the Arabian Peninsula, as well as the Houthi fighters.