The tall ship Picton Castle has called off its search for crew member Laura Gainey, swept overboard last week.

"It was our most fierce hope to find Laura alive,'' wrote Capt. Daniel Moreland in a statement on Tuesday.

He told The Canadian Press that the crew tried for more than 80 hours to find Gainey.

She is the daughter of Bob Gainey, general manager of the Montreal Canadiens.

The vessel continued searching even after the U.S. Coast Guard announced Monday evening that it was suspending search efforts.

The Picton Castle had been en route to the Caribbean island of Grenada from its home port of Lunenburg, N.S. when it hit rough weather.

A rogue wave swept Gainey off the ship's rear deck last Friday evening. The incident occurred about 760 kilometres east of Cape Cod, Mass.

Moreland said the ship's crew is grief-stricken by the event.

"The time has now come to end the search and allow our crew to carry on with the voyage southward towards calmer, safer waters."

The 25-year-old, who had a tall ship tattooed on her left shoulder, wasn't wearing a lifejacket. Nor was she tethered to the vessel by a safety line. Actually, she wasn't even on duty at the time.

"It is not out of the (ordinary) for a crew member who is not on watch to go up on deck,'' said Susan Corkum-Greek, a Lunenburg resident who is helping the crew members.

"As to what she was specifically doing, we can't say for certain.''

However, Canadian safety officials say any formal investigation will have to come from authorities in the Cook Islands where the vessel is registered.

The Cook Islands are located halfway between Hawaii and New Zealand.

A Vancouver-based spokesperson for the International Transport Worker's Federation said Canada should still launch a probe.

"The Cook Islands? ... It's just a little set of islands that has no resources. What the Cook Islanders are doing is basically renting out their flag. They haven't got a maritime organization that can fly around the world," Pete Lahay told  The Canadian Press.

There is a cautionary tale in this tragedy for Canadians who sail on foreign-flagged vessels, he said.

"I think something like this ought to be looked at,'' said Lahay. "It's a tragedy, but do we repeat our mistakes? Or do we learn from them?''

Corkum-Greek said the Picton Castle meets or exceeds regulations for Canadian sail-training ships.

Earlier Tuesday, the Gainey family thanked all those who tried to find Laura in the mid-Atlantic.

"We wish to sincerely thank all the people who have been involved in the search for our darling Laura," said the statement, released through the Montreal Canadiens hockey club.

"Their extensive efforts and their tremendous support throughout this ordeal will never be forgotten. We would particularly like to thank the United States Coast Guard and the Canadian Forces' Joint Rescue Co-ordination Center in Halifax for their extraordinary efforts.

"We are also very grateful to the entire crew of the Picton Castle and the merchant ships that graciously volunteered their time and resources."

The family also expressed gratitude for the "overwhelming support and prayers" received from not only family and friends, but the public too.

With files from The Canadian Press