The three couples, in their 50s, were among more than 200 passengers evacuated, many on lifeboats, after the blaze in the engine room sent smoke billowing through the ship.
The flames were so intense they left two crewmen dead and at least a dozen injured.
They also damaged the hull of the 11,000 ton MS Nordlys, allowing seawater to leak into the ship, and causing it to list dangerously as it limped into port.
The £1,000 cruise, operating on a popular 1,500 mile tourist route from Bergen, southwest Norway, to the Russian borders above the Polar circle, was off the coast of Alesund, western Norway, when disaster struck at around 9am.
Passengers noticed smoke coming from the lower decks of the boat before the alarm was sounded and they were ordered onto deck to be evacuated, many on lifeboats.
The boat, with smoke pouring out of the stern, limped into the harbour where the remaining passengers and crew were removed from the vessel.
It was there that the dead were discovered and the injured suffering from burns and smoke inhalation were taken to hospital.
“Our suspicion is that there has been an explosion in the machine room,” Police Chief Yngve Skovly.
He said all 207 passengers – and most of the crew of 55 – on board the MS Nordlys are now accounted for.
Geir Thorsen, head of the fire brigade in Alesund, said they are now in control of the fire, but the ship is taking in water.
Danielle Passebois-Paya, from southern France, said she and other passengers were having breakfast when they noticed what they thought was cigarette smoke coming from the kitchen.
“Then the alarm went and we were told to get up on deck,” she said. Then we saw smoke coming up from the ship.
“We were sent up on deck and were given life jackets.
“It took a few minutes from the alarm went, until we put in the lifeboats. When we were let down in the lifeboats, we could see the smoke roll out of the chimney of the boat.
“The crew did a very good job. The evacuation was well-organised. Everything was very quiet, and there was no panic.”
Harald Sundberg, 33, from Bergen said: “I sat and ate breakfast with a couple from Australia. They asked if I noticed a strange smell. I did. When I turned, I saw smoke roll out from the kitchen.
“At first he thought it was something that was burning in the kitchen. But I knew it was a chemical smell in the smoke.
“We got up and walked out. But the smoke was just thicker and thicker.”
Olav Fjell, chief executive of the boat operator Hurtigruten, expressed his sorrow at the death of his crew.
“It’s so hard to get the message that we have lost two colleagues,” he said.
“Losing a friend is terribly sad. We are not such a big business and everyone knows everyone.”
Thorsen described the fire as “big and intense”.
He could not confirm reports that the fire-extinguishing system on-board the ship did not work, but said the electricity system was knocked out.
“There are no indications that the fire had spread to other rooms in the ship,” he said.
Petra Sestak, at Hurtigruten, said the surviving passengers, who were put up in a nearby hotel, would now have the choice whether to board a new cruise or return home.