The woman, who was wearing a wetsuit, was attacked while swimming along the coast near the city of Portland.
Maine Department of Marine Resources official Patrick Keliher said kayakers then brought her back to shore, where she was pronounced dead.
First fatal attack in Maine
The victim was identified by authorities as 63-year-old Julie Dimperio Holowach, who lived in New York City and owned a residence on the coast in Maine.
A tooth collected at the scene confirmed that it was indeed a great white shark. This is the second shark attack on record in Maine, where the water is cold for swimming, and the first fatal.
Sharks spotted near New York
The local Department of Agriculture and Forestry has ordered bathers to stop when they have waist-deep water in the ten state parks that have a beach, a spokesperson said.
The Maine Department of Marine Resources advised him not to swim near seals or schools of fish, which are often the initial targets of sharks. For several weeks, sharks have been seen in several places on the northeast coast of the United States, especially near New York.
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