A German woman who had her arm bitten off by a shark in Hawaii has died a week later from her injuries.

Jana Lutteropp, 20, had her right arm bitten off while snorkelling off Palauea Beach in Makena, Maui County. She spent a week in critical condition at Maui Memorial Medical Center before dying as a result of her injuries.

Her family said Lutteropp had "fought hard to stay alive" before confirming she had died in a statement.

Her mother Jutta Lutteropp and sister Julia Broeske added: "Jana was a very beautiful, strong, young woman who was always laughing, and we will forever remember her that way."

Lutteropp was originally pulled from the water following the shark attack by a high school teacher who heard her screams. Rick Moore, 57, said Lutteropp went in and out of consciousness and kept repeating that she was going to die.

It is not known what type of shark had bitten her.

Lutteropp had travelled to Hawaii after finishing her year as an au pair, according to Cultural Care Au Pair, the agency she'd worked with.

The agency offered their condolences to Lutteropp, saying: "We are deeply saddened at the news that a Cultural Care au pair travelling after completing her year was gravely injured in a shark attack in Hawaii. Despite the best efforts of medical teams, Jana of Germany passed away from her injuries today surrounded by her family. Please join us in keeping them in your thoughts and prayers."

William Aila, head of the State Department of Land and Natural Resources, the agency responsible for Hawaii's waters, also extended his sympathy to her family and friends.

He said: "As an island state, we are aware that we are all visitors in the natural environment that surrounds us, and that unfortunate incidents such as this one can occur. We are committed to furthering research efforts that will help guide effective management actions in the interest of safety."

The attack on Lutteropp was the eighth shark attack in Hawaiian waters this year and tenth in 2012. The US state usually sees only three to four attacks each year.

The family asked that donations in her memory be made to the Maui Memorial Medical Center Foundation.