
The announcement by Italian-Swiss giant MSC and France's CMA CGM follows a similar decision Friday by two of the world's largest shipping companies, Maersk and Hapag-Lloyd.
The announcements were in response to a warning by the Iran-backed Huthi rebels, who control much of Yemen but are not recognised internationally.
The Huthis said they were targeting vessels near the strategic Bab al-Mandeb strait to pressure Israel over its devastating war with Palestinian Hamas militants in the Gaza Strip.
Thousands of ships every year transit 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.
Ships belonging to Israel or heading to its ports "will remain vulnerable to targeting until the aggression stops, the siege on Gaza is lifted, and humanitarian aid continues to flow" to Gaza, Huthi spokesperson Mohammed Abdul Salam said on X, formerly Twitter.
Comment: This is important, because it's not all ships travelling through the passage that will be targeted. And this is confirmed by the recent attacks that were only on those owned by Israeli citizens, or travelling to/from Israel: Two ships hit in Red Sea from Yemen, several ships prevented from reaching Israel
Oman was sponsoring discussions "with a number of international parties" regarding operations in the Red and Arabian Seas, he added.
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.
The UK government said one of its destroyers had also brought down a suspected attack drone in the area.
'Situation continues to deteriorate'
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.
On Friday, the International Chamber of Shipping condemned the Huthi attacks which "threaten the lives of innocent seafarers and the safety of merchant shipping".
The incidents breached international law and states in the region should work to de-escalate the situation, it said.
Comment: And what of the concerns of the Houthis? Israeli bulldozers crushed and 'buried alive' dozens as it rolled over tents at Gaza hospital
Diverting Asia-bound shipping from the Red Sea to South Africa's Cape of Good Hope would increase costs and delays, the body noted.
Consultancy S&P Global estimated that the detour would increase the distance between Rotterdam in the Netherlands and Singapore by 40 percent.
Comment: Whilst this exposes just how incapable of responding to the situation the establishment is, it also may be considered by some factions in the West to be a beneficial turn of events because it's clear that some are working to, incrementally, disrupt the supply chain, both to sabotage the economies of the East but also to further impoverish the people in their own: UK facing food shortages & more price rises as Panama Canal drought worsens