Mr Houthi has appeared in a video showing him uninjured
The leader of the Houthi rebels in northern Yemen has offered to withdraw their remaining fighters from neighbouring Saudi Arabia.
The rebels crossed the border and took control of a mountainous region in November last year.
Earlier in January, the Saudi military said they had driven the rebels across the border, but the rebels denied this.
Rebel leader Abdul-Malik al-Houthi, has now said they will withdraw to prevent further civilian casualties.
Appearing in an audio message posted to the Houthi rebels' website, Mr Houthi called the move "an initiative".
"If the Saudi regime maintains its aggression after this initiative, it would be showing that its intention is not to defend its territory, but to invade our borders," he said.
He threatened "open war" on "many fronts" if the Saudis did not allow the Houthis to return to Yemen.
Last week Mr Houthi appeared in a video apparently showing him unharmed after Yemeni officials claimed he had been killed.
Houthi forces entered Saudi Arabia in November after making several accusations that the government in Riyadh was aiding the Yemeni government in their campaign against the rebels.
Fighting between members of the minority Shia Zaidi sect and the state has occurred sporadically since 2004.
The rebels accuse the Yemeni government of social, economic and religious marginalisation.
Alongside the fighting in the north and a secessionist movement in the south, Western policymakers believe al-Qaeda is gaining a foothold in Yemen.
In early January, US Secretary of State Hillary Clinton said instability in Yemen was a global as well as regional threat.
The conflict in the north has forced 200,000 people top flee their homes, aid agencies say.