Denmark's Maersk (MAERSKb.CO) and German rival Hapag-Lloyd (HLAG.DE) said on Tuesday their container ships would continue to avoid the Red Sea route that gives access to the Suez Canal following a weekend attack on one of Maersk's vessels.

Both shipping giants have been re-routing some sailings via Africa's southern Cape of Good Hope as Yemen-based Houthi militants attack cargo vessels in the Red Sea. The disruption threatens to drive up delivery costs for goods, raising fears it could trigger a fresh bout of global inflation.

Maersk had on Sunday paused all Red Sea sailings for 48 hours following attempts by Yemen-based Houthi militants to board the Maersk Hangzhou. U.S. military helicopters repelled the assault and killed 10 of the attackers.

"An investigation into the incident is ongoing and we will continue to pause all cargo movement through the area while we further assess the constantly evolving situation," Maersk said in a statement.

"In cases where it makes most sense for our customers, vessels will be rerouted and continue their journey around the Cape of Good Hope."

Maersk had more than 30 container vessels set to sail through Suez via the Red Sea, an advisory on Monday showed, while 17 other voyages were put on hold.

Hapag-Lloyd (HLAG.DE) said its vessels would continue to divert away from the Red Sea - sailing instead via Africa's southern tip - until at least Jan. 9, when it will decide whether to continue re-routing its ships.

"In cases where it makes most sense for our customers, vessels will be rerouted and continue their journey around the Cape of Good Hope."

Maersk had more than 30 container vessels set to sail through Suez via the Red Sea, an advisory on Monday showed, while 17 other voyages were put on hold.

Hapag-Lloyd (HLAG.DE) said its vessels would continue to divert away from the Red Sea - sailing instead via Africa's southern tip - until at least Jan. 9, when it will decide whether to continue re-routing its ships.