Two major freight firms including MSC, the world's biggest container shipping line, on Saturday said they would avoid the Suez Canal as Houthi militants in Yemen stepped up their assaults on commercial vessels in the Red Sea.

Yemen's Iranian-backed Houthi movement has been attacking vessels in response to the Gaza war on a route that allows East-West trade, especially of oil, to use the Suez Canal to save the time and expense of circumnavigating Africa. War risk insurance premiums have risen as a result.

The Liberian-flagged MSC Palatium III was attacked on Friday with a drone in the Bab al-Mandab Strait off Yemen, at the southern end of the Red Sea, according to the Houthis.

No injuries were reported, but the vessel suffered some fire damage and was taken out of service, MSC said in a statement. Another Liberian-flagged vessel, Hapag Lloyd's Al Jasrah, was hit by a missile, the U.S. military said.

Denmark's A.P. Moller-Maersk on Friday paused all its container shipments through Bab al-Mandab until further notice, and was joined on Saturday by the Swiss-based MSC and French shipping group CMA CGM.

"The situation is further deteriorating and concern for safety is increasing," CMA CGM said in a statement.

German container line Hapag Lloyd has said it might do the same.

HOUTHIS ATTACK EILAT IN ISRAEL

The Houthis have in recent weeks stepped up attacks on shipping and also fired drones and missiles towards Israel - on Saturday hitting the Red Sea resort city of Eilat - in support of the Iranian-backed Palestinian Islamist Hamas group fighting Israel in Gaza.

U.S. Central Command said the guided-missile destroyer Carney had shot down 14 drones launched by the Houthis in the Red Sea on Saturday morning.

In a statement, it said they were assessed to be one-way attack drones and had been shot down with no damage to ships.

Britain also said one of its warships had shot down a suspected attack drone targeting merchant shipping.

The Houthis, who rule much of Yemen, have pledged to continue their attacks until Israel stops its offensive, but said on Friday they were targeting only ships heading for Israel.

However, both the Palatium III and another MSC ship that was threatened, the Alanya, listed Jeddah in Saudi Arabia as their destination, based on data from the ship tracking and maritime analytics provider MarineTraffic.

On Saturday, a Houthi spokesman said the group has engaged in Oman-mediated talks with unnamed "international parties" over its operations in the Red Sea and Arabian Sea - which could indicate the Houthis may be willing to deescalate.

Bab al-Mandab is one of the world's most important routes for global seaborne commodity shipments, particularly crude oil and fuel from the Gulf bound westward for the Mediterranean via the Suez Canal or the nearby SUMED pipeline, as well as commodities heading eastward for Asia, including Russian oil.

The rise in Red Sea war risk premiums translates into tens of thousands of dollars of extra costs for a seven-day voyage.

MSC said it would reroute some services around the Cape of Good Hope on Africa's southern tip, adding days to the sailing times of vessels booked to transit the Suez Canal.

(Reporting by Gursimran Kaur in Bengaluru and Mathieu Rosemain in Paris; Writing by Kevin Liffey and Hatem Maher; Editing by Jane Merriman and David Holmes)