The group also announced a three-day suspension of ground offensive operations in Yemen, including in the gas producing region of Marib, said Mahdi al-Mashat, the head of the Houthis' political office, in a speech broadcast on television.
The unilateral initiative came as violence between the Iran-aligned group and the Saudi-led coalition, which have been at war since 2015, escalated dramatically this month.
Air strikes of the Saudi-led coalition pounded the Houthi-controlled sea ports of Hodeidah and Salif on Saturday, a day after the group launched broad attacks on Saudi Arabia, including on an oil facility in Jeddah, causing a massive fire and a huge plume of black smoke.
Eight people were reportedly killed.
Lifting restrictions imposed by the coalition's warships on the Red Sea Yemeni ports has been a major condition from the Houthis for a ceasefire. Saudi Arabia says there is no blockade on the ports and it is only preventing arms smuggling.
Mashat said Saturday's initiative would last if the coalition reopened the ports and stopped its air strikes. In exchange for extending the suspension of ground offensive operations, he said Saudi Arabia must announce a withdrawal of foreign troops from Yemen and stop supporting local militias.
It is unlikely that the kingdom would agree to such conditions, as Riyadh seeks an inclusive ceasefire simultaneously with reopening the ports and Sanaa airport.
Mashat added the group was ready to release all prisoners, including the brother of Yemen's President Abd-Rabbu Mansour Hadi.
The United Nations is also trying to secure a temporary truce for the Muslim holy month of Ramadan that starts in April, and ahead of Riyadh's hosting Yemeni parties for consultations later this month.
