It comes after the US announced the formation of a military alliance to counter the attacks, raising questions as to how this will succeed.
Among the latest firms to announce it has temporarily ended its shipping services from the Bab al-Mandab Strait to the Suez Canal that covers the Red Sea is the oil giant British Petroleum (BP).
"The safety and security of our people and those working on our behalf is BP's priority," the firm said.
"In light of the deteriorating security situation for shipping in the Red Sea, BP has decided to temporarily pause all transits through the Red Sea."
BP's decision followed in the footsteps of the world's largest container carrier line, the Swiss-based MSC, which on Saturday said it would avoid the Suez Canal, after Ansarullah forces struck one of their container vessels.
"Until the Red Sea passage is safe, MSC ships will not transit the Suez Canal Eastbound and Westbound. Already now, some services will be rerouted to go via the Cape of Good Hope instead," MSC said.
Another large shipping group, the Danish-based Maersk, has suspended sailing its container ships in the waters until further notice.
The prominent container shipment line said in a statement on Friday that "following the near-miss incident involving Maersk Gibraltar yesterday and yet another attack on a container vessel today, we have instructed all Maersk vessels in the area bound to pass through the Bab al-Mandab Strait to pause their journey until further notice."
French group CMA CGM has revealed it is also avoiding the Red Sea.
Other shipping giants such as Hapag-Lloyd, which had seen one of its ships targeted last week, joined the list on Monday evening, saying "for the time being, we are routing ships around the Cape of Good Hope".
"We ask for your understanding under these serious circumstances", the container ship firm told its clients.
More firms have told all vessels scheduled to pass through the Bab al-Mandab Strait to pause their journeys until further notice.
The Norway-based oil tanker group Frontline has said its vessels will avoid passages through the Red Sea and the Gulf of Aden for the time being.
China's Evergreen announced that it had temporarily suspended import and export services in Israel until further notice, citing the security risk, in addition to halting journeys via the Suez Canal.
Evergreen Line said on Monday that it had decided to "temporarily stop" accepting Israeli cargo with immediate effect.
On Saturday, Hong Kong-headquartered container group OOCL said that "due to operational issues," it would stop accepting cargo to and from Israel until further notice.
Ansarullah, which supports the Palestinian resistance in the Israeli war on Gaza, has vowed to target all vessels that are heading to and from the occupying regime.
The movement has launched a series of attacks on vessels in the Red Sea, as well as launching drones and missiles targeting Israeli military sites in the occupied Palestinian territories.
The attacks have also put more pressure on other companies still providing sea transport to the regime.
Experts say the ongoing attacks by Ansarullah on Israeli-linked vessels in the Red Sea will see more shipping firms halt their passage via the Red Sea.
The maritime disruption has also been blamed for a rise in global oil prices estimated at around 3%.
The Suez Canal is a key route for global trade, in particular for the transport of oil, grain and consumer goods. About 15% of world shipping traffic transits via the Canal, the shortest shipping route between Europe and Asia.
All ships that want to transit the Canal must navigate their way through the Red Sea and crucially the vital Bab al-Mandab Strait, a small strip of the Red Sea that separates Yemen from Djibouti and Eritrea.
The disruption to normal trade flows is set to result in higher prices and delays, which will only extend the longevity of the disruption, as different shipping routes will add thousands of kilometers to a vessel's journey.
Firms are reportedly sailing around Africa instead, which typically adds nearly 5,000 kilometers to a ship's journey.
That can take up to an additional 14 days for the cargo to reach its intended destination and raise the costs of shipping for consumers.
"War risk insurance premiums are on the rise naturally, but as vessels get rerouted around Africa, shipping supply will be tighter as cargoes travel longer," Frontline CEO Lars Barstad told Reuters. "That would put rates under a strong upwards pressure."
"For ships heading to the (Israeli regime) from Asia, the route around Africa is significantly longer - about 7,000 nautical miles and 10-14 days - than via the Suez Canal. This route also incurs higher fuel costs," Freightos CEO Zvi Schreiber said.
Maersk also said it would apply an "emergency risk surcharge" for all cargo discharged at Israeli terminals.
The regime's own container firm Zim said it had "witnessed an increase in the level of the threat," prompting higher surcharges on its ships, which included charges to Israeli-occupied ports from Asia.
Vessels that are, at the moment, still docking at the regime's biggest ports of Ashdod in the south and Haifa in the north have been switching off their tracking transponders to avoid detection, shipping sources said.
"Ship operators which have called, or plan to call, [at] Israeli ports should limit information access," an advisory issued by leading global shipping associations read. "Published information could be used by (the Ansarullah)."
The cost of shipping goods to the Israeli regime by sea has risen in recent days as some container lines pull out while others impose new surcharges, adding to the regime's supply chain pressures amid its war on Gaza, shipping sources said.
The regime, whose economy relies on seaborne trade, has not said whether it will cover the additional shipping costs.
Speaking in Bahrain, home to the US Navy's headquarters in West Asia, US. Secretary of Defense, Lloyd Austin, announced the creation of a multi-national military coalition to safeguard the Red Sea waters.
US warships will join others from the UK, Bahrain, Canada, France, Italy, Netherlands, Norway, the Seychelles, and Spain.
Other countries will also contribute to the alliance but have chosen to remain anonymous, the AP news agency reported, citing an official. The official spokesman for Ansarallah, Muhammad Abdel Salam, stressed on Tuesday that the US-formed coalition is aimed at protecting the Israeli regime.
"It will not stop Yemen from continuing its legitimate operations in support of Gaza, stressing that whoever seeks to expand the conflict will bear the consequences," Abdel Salam noted.
Abdul Salam concluded by saying that "just as America allowed itself to support the regime, the people of the region have full legitimacy to support the Palestinians and Yemen has taken it upon itself to stand by the Palestinian right and the great injustice in Gaza."
Experts have pointed out that just as Ansarullah targeted commercial tankers heading to the Israeli regime, the movement has also been targeting American warships with drones and missiles.
It will prove very difficult for a US-led alliance to stop Ansarullah attacks. Militarizing the Red Sea further will not bring security to the region as Ansarullah may raise the level of its attacks.
This will not provide the protection needed for ships to dock at Israeli ports.
It will likely put even more pressure on the regime to end its war on Gaza.
Analysts believe it could also widen the war. Should the US strike at Yemeni territory, and Ansarullah start its retaliatory attacks, no ships will sail anywhere near the Red Sea for the foreseeable future.
In addition, war with Yemen is an unlikely option because the US, together with its Arab allies, has already fought a deadly war with Ansarullah to no avail. During its military campaign against Yemen, Saudi Arabia enjoyed strong backing from the US. Therefore, the US. is not new to war in Yemen. It knows full well that war in Yemen is not an option given the prowess of the Yemenis.
MNA/