SYDNEY, June 13 (Reuters) - A woman swimmer was seriously injured in a shark attack at a Sydney beach on Saturday, authorities said, in the latest of a spate of shark attacks off Australia's coast.

Emergency services were called to Coogee Beach in the east of Sydney, Australia's largest city, in the morning on reports that the 30-year-old had been bitten, police said in a statement.

"The woman was pulled from the water by members of the public who commenced first aid," police said, adding that the victim suffered serious arm and leg injuries.

"She has large flesh wounds to the leg and the arms that are going to require a lot of surgery," New South Wales Ambulance Inspector Mike Corlis told reporters at Coogee Beach.

"We'll be working closely with the New South Wales government, awaiting instruction as to when it is safe to reopen," council mayor Dylan Parker told reporters.

A witness to the attack, Nicola Logan, told Reuters at Coogee Beach that she saw a "massive pool of blood" in the water, then "a lady kind of motioning to swim, lots of splashing, and then a ski paddler was out trying to bring her in".

A week earlier, a man died after being attacked by a shark while fishing off ​the coast of Western Australia state, in the latest fatal incident.

Dozens of beaches along Australia's east coast, including in Sydney, were closed in January ⁠after ​four shark attacks in two days. Those followed heavy rain that created murky water, attracting sharks and reducing their ​visibility.

Most shark attacks occur along the east and southeast seaboard of Australia, which ⁠averages ​around 20 such incidents a ​year, according to the Australian Institute of Health and Welfare.

(Reporting by Sam McKeith and Christine Chen in Sydney; Editing by William Mallard)