An Egyptian government environmental agency claims Cunard's Royal Viking Sun luxury cruise liner caused the damage when it went aground last week.
Cunard has been told the 37,845-ton vessel is being held in the Red Sea port of Sharm el-Sheikh until the compensation dispute is resolved. Cunard is sending out its own diver to check damage to the coral reef.
The ship, which had 560 passengers on board, including 54 Britons, was heading towards the Jordanian port of Aqaba when it apparently struck the reef.
She lost all power and had to be towed into Sharm el-Sheikh where Cunard is carrying out temporary repairs.
Egypt is claiming that the Royal Viking Sun has damaged 2,000 cubic metres of coral reef and sea life at the Ras Mohamed Nature Reserve at the southern tip of the Sinai peninsula.
"Several vessels are known to have hit the reef in the last few years and it should be possible to tell just how old the damage is," said Bill Spears, Cunard's public relations director .
The passengers on the stricken vessel flew home at the end of last week.
Cunard said that it hoped to have the Royal Viking Sun back in service in time for its European cruise from France on 8 June.