However, due to harsh weather conditions and other "inherent challenges associated with conducting towing operations in open seas," it's impossible to predict the exact arrival time, the Navy said in a statement.
"This is a difficult operation in a challenging environment. I'm pleased with what has been achieved so far with the help of our USN colleagues," said Commodore Bob Auchterlonie, the commander of the navy’s Pacific fleet.
The 44-year-old vessel was crippled by an engine room fire Thursday night while en route from Hawaii to its home port of Esquimalt, on Vancouver Island.
The fire left the ship dead in heavy seas about 630-kilometres northeast of Hawaii with nearly 300 people onboard, including 17 family members of the crew. Twenty crewmembers suffered minor injuries fighting the blaze.
The Navy said there are reports of "significant fire and heat damage" to the ship's engine room and "considerable heat and smoke damage" in surrounding compartments.
"The living conditions on board are austere as a result of the damage sustained during the fire," it said.
The ship will be thoroughly examined once it arrives in Hawaii, and the cause of the fire will be investigated, it said.
The USS Chosin, a guided missile cruiser, delivered fresh supplies to Protecteur Saturday, and the American destroyer USS Michael Murphy helped transfer family members from Protecteur, the Navy said.
Auchterlonie said the stranded ship is being towed to Hawaii by the cruiser and a U.S. Navy tug.
As for conditions aboard Protecteur, Auchterlonie quotes the vessel’s commanding officer as saying the crew is “making the best of a crappy situation.”