If Saudi Arabia continues its air strikes, blockade and aggression against Yemen, the Houthis will respond in a "more painful, deadly and destructive", the group's leader warned on Friday.
Addressing Al-Masirah TV on the fifth anniversary of the 21 September Revolution, Abdul Malik Al-Houthi warned Saudi against the "ongoing shelling, blockade and aggression" in Yemen.
The remarks follow drone and missile strikes against Saudi's Aramco busiest oil facilities in the eastern province, which temporarily shut down production at Abqaiq and Khurais.
The Houthis claim of responsibility has been rejected by the US and the Saudis who point the finger at Iran. Claims Tehran has strenuously denied.
The group has called for an end to hostilities with President of the Supreme Political Council Mahdi Al-Mashat announcing a halt to strikes in Saudi territory on the condition that the kingdom stops its military actions in Yemen.
This peace initiative has been welcomed by the UN's special envoy for Yemen, Martin Griffiths, who declared that the offer "could send a powerful message of the will to end the war".
However, current events suggest that the Saudis have not accepted the initiative following air strikes yesterday in the province of Amran, one of which killed seven members of the same family including children who were seeking shelter in a mosque.
The Houthis have previously threatened to re-new air strikes following the Aramco attack and warned foreigners to avoid oil facilities in the kingdom.