Huthi militias in Yemen have crossed a "red line" and will pay a high price for their deadly bombardments of Saudi Arabia, the Saudi-led coalition said on Thursday.

"The equation is different, the confrontation is different, and they will pay a harsh and expensive price," coalition spokesman Brigadier General Ahmed al-Assiri told reporters.

"The safety of Saudi Arabia is a top priority for the coalition and the Saudi armed forces. It is a red line they crossed."