In a post on his Twitter account on Wednesday, Mohammad Abdul-Salam said his movement has sent to the UN a comprehensive vision which includes an end to the five-year war and to the blockade imposed on Yemen.
"(Our proposal) will lay the foundations for a political dialogue and a transitional period," he added.
It came after the Saudi-UAE coalition launching a military campaign against Yemen declared a unilateral ceasefire.
The suspension of the coalition's military operations is expected to go into effect at 12 pm local time (09:00 GMT) on Thursday and last for two weeks.
The announcement came days after the United Nations called for a halt in hostilities amid the coronavirus pandemic.
The ceasefire is reportedly intended to help prevent a coronavirus outbreak in Yemen, while also allowing for de-escalation in the fighting and giving the Houthis an opportunity to join UN-sponsored talks on a settlement to the conflict, Al Jazeera reported.
Last week, UN special envoy Martin Griffiths sent a proposal to the warring parties calling for a nationwide ceasefire, including halting all air, ground and naval hostilities, and for the parties to ensure compliance by forces on front lines.
The Saudi-led war on Yemen has killed more than 100,000 people and unleashed an urgent humanitarian crisis that has pushed millions to the verge of famine and forced thousands to seek shelter in displacement camps.