Early on, the Houthi rebels were known for attacking important Saudi oil refineries. Now they apparently want to end their drone and missile attacks on Saudi Arabia - under certain conditions.
"We hope that Riyadh will respond positively to the initiative," said Mahdi al-Mashat, president of the Huthis Supreme Political Council in a televised speech.
However, should Saudi Arabia continue with its bombing and air strikes, the Houthis would have the right to respond, warned its political leader.
The Houthis had become aware of the attacks on important oil facilities in Saudi Arabia last weekend. However, the US and Saudi Arabia blame Iran for the attacks. The attacks with drones and cruise missiles had at times halved Saudi Arabia's oil production.
In his televised speech, Al-Mashat demanded that the Sanaa airport blockade be stopped immediately and that ships in the Hudaida port no longer be intercepted.
The Houthis had taken the Yemeni capital Sanaa five years ago. They control large parts of the North Yemen. Shortly thereafter, Saudi Arabia joined other Arab states in the conflict. The United Nations describes the conflict in Yemen as the currently worst humanitarian crisis in the world.