Houthis have said they pose no threat to international shipping but have reiterated their intention to target vessels from Saudi Arabia.
Saudi Arabia has increasingly relied on the Red Sea for oil exports since the US and Israel's war effectively closed the Strait of Hormuz.
At least 46,000 people have been displaced in Yemen since fighting escalated last week, according to the United Nations.
BBC Verify's Thomas Copeland reports.
Produced by Aisha Sembhi. Graphics by Mark Edwards.
