Almost 1,000 survivors were on board the cargo ships which went to the rescue. They faced a two-day passage to the Seychelles in primitive conditions.
An Englishman, identified as Edward Morris, 68, died during the rescue and another person was reported to be unaccounted for from the 581 passengers - including about 90 Britons - and 404 crew.
The Achille Lauro, scene of a hostage drama in 1985, was sailing from Genoa to South Africa by way of Israel, Egypt and the Seychelles when fire broke out in the engine room at about 1am yesterday.
Half an hour later, the engines stopped and passengers were told to go on deck to await orders to evacuate. Once the evacuation was ordered, the ship began to list heavily but at least 60 crew members stayed behind to fight the fire.
Ola Vaage, of the Norwegian rescue centre Stavanger, which organised the rescue ships via satellite, told the Independent that a shortage of lifeboats in the Achille Lauro meant that up to 40 passengers had to remain on board the burning ship until lifeboats returned to pick them up after taking survivors to the Panamanian tanker Hawaiian King, the Liberian-registered Bardu and a Greek ship, the Treasure Island. Some passengers reported that they had to wait seven hours.
It was not clear whether the lifeboats were inaccessable because of the ship's 30-degree list or whether there simply were not enough - a charge vehemently denied by the Italian marine rescue centre in Rome.
Norwegian officials accused Italian marine rescue officials who later took over the emergency of failing to pass on urgent requests to have drugs and blood delivered by US Navy helicopters. That claim was angrily denied by the Italian owners of the ship, Star Laura.
Mr Vaage said requests for insulin, blood plasma and anti-Parkinson's agents were not passed to the US naval base in Bahrain by the Italian authorities several hours after the request was relayed to them from the Bardu.
But a Star Laura official said: ''The drugs are not important. There are no problems only one person has diabetes and [insulin] was delivered by a US helicopter.''
Mr Vaage said a US helicopter eventually delivered food and medicine to Hawaiian King and Bardu, but only after the US rescue centre in Bahrain was contacted directly by the Norwegian authorities. ''The Italians had the information for several hours after we handed over control but they did not react and we had to intervene directly.''
Two US naval vessels with emergency medical facilities were within hours of joining the rescue flotilla last night.
A helicopter from the cruiser USS Gettysburg had earlier lowered emergency ''meals-ready-to-eat'', drinking water and other supplies to the Hawaiian King, which picked up more than 800 survivors.
A US helicopter pilot, Lieutenant Paul Frost, reported yesterday afternoon: ''The whole aft half of the [Achille Lauro] is fully engulfed by flames.'' She was in imminent danger of sinking, he said.
The 23,478-ton vessel was built in 1947 as the Willem Ruys. In 1985 she was hijacked by Palestinians who killed a disabled American passenger, Leon Klinghoffer. US warplanes intercepted an aircraft in which the hijackers were fleeing, forcing it to land at a Nato airbase.