The announcement by Italian-Swiss giant MSC and France's CMA CGM follows a similar decision on Friday by two of the world's largest shipping companies, Maersk and Hapag-Lloyd, in response to a warning by the Iran-backed Huthi rebels.

The Huthis, who control much of Yemen but are not recognised internationally, said they were targeting vessels near the strategic Bab al-Mandab strait to pressure Israel over its devastating war with Palestinian Hamas militants in the Gaza Strip.

Forty percent of the world's international trade transits through the strait, which runs between Yemen, on the southwestern tip of the Arabian Peninsula, and the African continent.

The tensions have added to fears that the Gaza conflict could spread.

An American destroyer on Saturday shot down more than a dozen drones in the Red Sea launched from Huthi-controlled areas of Yemen, the US Central Command (CENTCOM) said.

And the UK government said one of its destroyers had also brought down a suspected attack drone in the area.

MSC, one of the world's largest freight shipping lines, said one of its container vessels had been targeted in the Red Sea on Friday and it was halting traffic through the strait until it was safe. 

No one on the MSC Palatium III was wounded but the ship suffered fire damage, the company said.

CMA CGM said it had ordered all its vessels to leave the area and stay there until further notice.

"The situation continues to deteriorate and there are increasing concerns about security," it said.