Four-time Olympic gold medallist Betty Cuthbert has died aged 79, after a career which saw the sprinter set world records in several track events.

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She was dubbed the "golden girl" by the media after her performance at the 1956 Melbourne Olympics — where as an 18-year-old she won the 100 and 200-metre sprints.

Cuthbert was also a member of the victorious 4x100-metre relay team and became Australia's first triple gold medallist, achieving the feat just ahead of Murray Rose at the same Olympics.

She suffered a hamstring injury at the 1960 Olympics and announced her retirement from sport, but had a change of heart two years later.

She came back to win a fourth gold medal in the 400-metre event at the Tokyo Olympics in 1964.

WA Premier Mark McGowan has offered a state funeral for Cuthbert, who had multiple sclerosis and had used a wheelchair for many years.

"She was one of the greatest sportspeople in Australian history and I think the least we can do is offer a state funeral," Mr McGowan said.

"Australian sport always treasured her and her memory and I'd like to make sure the country and the state properly recognise her contribution."

Cuthbert was born in the Sydney suburb of Merrylands in 1938, a twin with her sister Marie, and moved to Western Australia several decades ago, where she lived in Mandurah, south of Perth.

Awarded a Member of the Order of Australia in 1984, Cuthbert was well known for campaigning to raise awareness of multiple sclerosis.

She had a rose named in her honour in 2010 for her work to help people with multiple sclerosis, and in 2014 the City of Mandurah opened Betty Cuthbert Park in the suburb of Halls Head.

She was a torch bearer at the Sydney Olympic Games' opening ceremony in 2000 along with her friend and fellow sprinter Raelene Boyle, who pushed Cuthbert's wheelchair during the ceremony.

An athlete of "humility and distinction"

Boyle described Cuthbert as a beautiful, poised and humble soul who never focused on the fact she had been the greatest in the world. She said her medals had been won "with humility and distinction".

"A lot of the athletes today could take a great deal of learning out of the way she did it," Boyle said.

Cuthbert carried the Olympic Torch at the Melbourne Cricket Ground in June 2004 in the lead-up to the Athens Games. ( Reuters: Dave Callow )

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Tennis player Margaret Court also paid tribute to Cuthbert, saying Australia had lost a sporting legend.

"We've lost a great sporting hero and a great Aussie," she said.

"She loved her nation. She'd been in a wheelchair for many years, but she never lost her spirit. She was just a great person."

Fellow runner Cathy Freeman joined Court and Boyle in paying tribute to the former athlete.

"Thank you for the inspirational memories, Betty Cuthbert. Rest in peace," she wrote.

Australian Olympic champion Marjorie Jackson-Nelson, who won sprinting gold medals four years before Cuthbert, said it was "a pleasure and a privilege to know Bet."

"She will be remembered for what she did for Melbourne I think particularly when the Olympics was on," she said.

"Most Australians would be sad to hear of Betty's passing, but her record will always live on."

The victorious Australian women's track relay team at the 1956 Olympics (l-r) Fleur Mellor, Norma Croker, Betty Cuthbert and Shirley Strickland. ( Supplied: National Archives of Australia )

Athletics Australia interim chief executive Michael Hall said Cuthbert was one of the greats of Australian sport and a genuine trailblazer for women in particular.

"Betty personified what it is about Australian sport - that if you're prepared to work hard and have a go, anything's possible," he said.

Sport Australia Hall of Fame chief executive John Bertrand said Cuthbert would forever be remembered as Australia's golden girl.

"Betty was a true inspiration and role model to all Australians. Her feats on the track brought together Australians as one. She loved the country and we loved her," he said.

Prime Minister Malcolm Turnbull said Cuthbert was "an inspiration and a champion on and off the track".

Opposition Leader Bill Shorten tweeted: "Rest in peace Betty Cuthbert, forever a golden girl."