The warning came after the Houthis fired missiles at Saudi Arabia, accusing the kingdom of bombing an airport under their control on Monday, marking a rupture in a four-year truce between the two sides.
The Iran-aligned Houthis have previously targeted Saudi energy infrastructure.
In 2019, they claimed responsibility for attacks on two key Saudi oil facilities that temporarily knocked out more than half of the kingdom's crude output.
In 2022, they struck Saudi energy facilities again.
At the time, the Saudi-led coalition said an Aramco petroleum products distribution station in Jeddah was hit and caught fire.
"The real equation is Sanaa airport for Riyadh airport, airports for airports, ports for ports, and blockade for blockade," the Houthi leader said in a televised speech.
Yemen has been mired in civil war for more than a decade since the Houthi rebels seized the capital Sanaa, prompting a Saudi-led military intervention in 2015 in support of the internationally recognised government.
The conflict has since evolved into one of the world's worst humanitarian crises, leaving the country divided between a Saudi-backed government in Aden and a Houthi administration in Sanaa.
