A South African Indian family of four was among hundreds of lucky survivors when a gigantic luxury cruiser ran aground off the coast of Italy last week.

What should have been a dream week-long holiday for Faizel Agjee, his wife Nafeesa and their teenage children Zaheer and Zahra turned into a nightmare just as they were about to sit down for dinner on the four-storey Costa Concordia when it started listing after hitting a reef off the west coast of Italy on Saturday.

The Costa Concordia was carrying more than 4,200 people when it ran aground shortly after starting a seven-day Mediterranean cruise on its way to Marseille in France and Barcelona in Spain, just as many passengers were having dinner.

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Carnival Corp, the parent company of Costa Concordia, put the initial cost of the disaster at $85-95 million.

Island residents have already said the ship was sailing far too close to Giglio and had hit a reef known as the School Rocks, well known to inhabitants.

The Corriere della Sera reported Monday that the captain had passed close to the island's rocky shores to please the head waiter who comes from Giglio.

It also quoted witnesses as claiming the waiter had warned Schettino just before the accident happened: "Careful, we are extremely close to the shore."

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Speaking to a local media from their temporary accommodation in Rome, the Agjees explained their experience as they ran from the dining room when it started tilting, jumped back onto the foundering ship from a lifeboat that was not working, and then ran through passageways together with other passengers, trying to hold on to anything firm to avoid slipping and falling.

Although the first announcement indicated that there was an electrical fault, the quick-thinking Zaheer got the family to run to their rooms first to gather their valuables and lifejackets, probably ensuring their safety.

Six others among the more than 4,000 people on board were not so lucky and lost their lives, while at least 70 were injured and 15 still listed as missing as rescue operations continued.

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"While waiting, many people continued to try and get on even though the boat was full to capacity; they pushed themselves through the gate, it was horrible," Zaheer was quoted as saying by The Star newspaper.

"The lifeboat could not be lowered and we had to jump back on to the ship; this was the most terrifying part of the entire night," Zaheer added.

Once back on the ship, the family held hands tightly and began a nerve-racking trip through the interior of the ship in search of another lifeboat.

"People were falling past us, crawling against the tilt, some were too scared to move," said Nafeesa.

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"Soon afterwards, a rescue vessel came towards us; its roof was in line with the deck and we had to jump on to the roof," said Faizal, who was hailed a hero by his family after he caught his sister during the jump, preventing her from falling far below.

The Agjees said they had to wait nearly three hours in icy temperatures before being taken to a Rome hotel, but were grateful for being alive and safe.

The family will return to their Pietermaritzburg home on Friday.

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Meanwhile, the 114,500-ton liner could be refloated with the help of huge inflatable buoys once the fuel is pumped out and leaks plugged, Costa Crociere said.

But company boss Foschi said the operation -- if it goes ahead -- would be "one of the most difficult in the world."

Passengers meanwhile described confusion on board as the lights went out and how they were at first told it was just an electrical fault -- before the ship lurched sharply on to its side and panic set in.

Some likened the disaster to the Titanic, which sank in the Atlantic with some 1,500 people on board on its maiden voyage in April 1912

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