Two children have been bitten while swimming in waters off New York state's Fire Island in what are thought to be the state’s first shark attacks for 70 years.

Police said they were investigating the two separate incidents, which took place at two beaches less than five miles apart on Wednesday.

A 12-year-old girl suffered bite marks “consistent with a large fish” while swimming at Sailors Haven beach and a 13-year-old boy on a bodyboard was taken to taken to hospital following an incident at nearby Atlantique beach, 50 miles east of Manhattan.

Paramedics removed a large tooth from the leg of the injured boy, which authorities are waiting for the state’s Department of Environmental Conservation to identify.

Less than a dozen such shark bites on people had previously been documented in New York state, with the last one coming in 1948, officials said.

The girl, Lola Pollina, said she was standing in waist-deep water when she suddenly felt a sharp pain, before noticing that her leg was "all bloody".

“I saw something next to me and I kind of felt pain and I saw a fin, I don't know how to describe it, and then I ran out of the water because I felt it,” she said at a press conference.

Shark caught on camera swimming in St Ives Harbour

“It was not that big, like three (0.91m) or four feet (1.22m).”

Democratic governor Andrew Cuomo released a statement saying he had ordered a multi-agency investigation into the possible shark attacks.

“I am relieved that both teenagers who were attacked have been released from the hospital,” Mr Cuomo said.

Lola Pollina, who suffered wounds on her right leg, was one of two children bitten in possible shark attacks off Fire Island beaches on Wednesday (AP)

“The state will do everything we can to protect beachgoers and keep the community safe.”

On Friday, a man in Fernandina, northern Florida, was hospitalised after being attacked by a nurse shark as he played with his son in less than two feet of water.

Minutes later, emergency services were also called to reports of a separate shark attack around a mile along the coast on a 17-year-old boy.