KEY WEST, Fla. — Endurance swimmer Penny Palfrey has abandoned her effort to become the first woman to swim unassisted from Cuba to the Florida Keys, ending her odyssey after almost 41 hours in the water and about three quarters of the way through the more than 100-mile swim, her support team said Sunday.

Andrea Woodburn, one of the team members, said by phone that the British-born Australian marathon swimmer halted her effort around midnight some 26 miles south of Key West because of a strong ocean current.

‘‘She is fine,’’ Woodburn said from Key West, without giving further details on Palfrey’s condition.

Woodburn said she had been in contact with Palfrey’s boat and was told the swimmer had to get out of the water when she encountered a strong current in the treacherous Florida Straits.

The waters in the area are notorious for their fickle currents, including the powerful Gulf Stream. But further details of whether she had encountered the Gulf Stream or a side eddy of that current were not immediately available.

Earlier in the day, Palfrey, 49, had been steady and strong and reported no physical complaints other than jellyfish stings, according to her support crew. She swam without the protection of a shark cage.

At about 8:30 p.m., roughly 37.5 hours into the swim, she was 76 miles from her starting point at a marina in the Cuban capital, according to her website’s GPS tracking report. At the time she was positioned about 30 miles south, southwest of Key West.

Previously, her personal best was 67 miles when she swam between Little Cayman and Grand Cayman islands last year, Woodburn said.