A fire that erupted aboard a Zim-operated containership has been fully extinguished after a week, according to vessel owner Danaos Corp.

The 4,253-teu Zim Kingston (built 2008) lost at least 109 boxes when it ran into stormy weather about 5 nautical miles (9.26 km) from the Port of Vancouver, according to the Canadian Coast Guard (CCG).

Several boxes containing hazardous mining chemical potassium amyl xanthate caught fire during the incident, two of which fell into the sea and have yet to be found.

Danaos has hired a contractor to search for the overboard containers, four of which were found on Thursday on the shores of Vancouver Island.

The CCG said some of the containers have fallen to the ocean floor.

"The specialised marine service company retained by the company to remove containers and debris from shores will begin the clean-up operation immediately," Danaos said in a statement.

"The company has been working closely with local authorities from the very first, committed to following all actions necessary to mitigate the consequences of the incident."

CCG's Unified Command is also looking for more containers from the Zim Kingston via aerial patrol.

The ship, which is carrying almost 2,000 containers, is anchored 4.7 nautical miles offshore while salvage experts start removing or securing damaged boxes now that the fire is fully extinguished.

Transport and Infrastructure Canada inspectors will then board the ship to determine and oversee any necessary repairs before directing it to a nearby port for unloading and further inspections.