Earlier Wednesday, Solomon Islands Broadcasting Corp. radio reported Ballard found the remains of the wooden boat, PT 109, lying on the seabed in the Blackett Strait near Gizo in the New Georgia group of islands in the Pacific Ocean.
Gizo is 235 miles northwest of the capital of the Solomons, Honiara.
The National Geographic Society in Washington Wednesday would only say the expedition had ended.
In that same statement, Ballard was quoted as saying, "While promising, the expedition findings are inconclusive at this time. We will review the results with naval experts over the next several weeks."
National Geographic said it will announce the results when the analysis is complete.
According to the radio report, Ballard — who led a team that found the Titanic shipwreck in 1985 — said he located the wreckage of Kennedy's boat last week after searching for about a week. He did not provide further details of the discovery, citing contractual obligations for film and magazine rights to the search.
Ballard could not be reached for comment. A worker at the Gizo hotel where Ballard had been staying told The Associated Press on Wednesday that the explorer left the islands.
The radio report said a National Geographic documentary will be released in November. Members of the National Geographic team in the Solomon Islands did not immediately return calls seeking comment.
The John Fitzgerald Kennedy Library and Museum in Boston had no information on the report. Ballard's Institute for Exploration at Mystic Marinelife Aquarium in Mystic, Conn., could not confirm the story.
Aquarium spokeswoman Lisa Jaccoma said, "They have found something. They're waiting to get confirmation of what they have found."
The PT 109 sank in August 1943 after it was hit by a Japanese warship.
It is unknown how much of the boat remains besides the engines. Water is expected to have caused extensive damage to the hull.
Ballard, who has located the wrecks of the Bismarck, USS Yorktown and Lusitania, had planned to use remote cameras to search for the boat.
The late president's brother, Sen. Edward M. Kennedy, a Massachusetts Democrat, and daughter, Caroline Kennedy, agreed to the expedition after being assured that the site would not be disturbed. Two members of Kennedy's crew died when the boat was hit.
In a 1999 interview, Ballard said PT 109 is "not lost, just misplaced." But he added that searching for the vessel in an area full of unexploded ordnance would be "no fun."
Kennedy was commanding a patrol in Aug. 2, 1943, when the boat was hit and cut in two by a Japanese destroyer.
Kennedy and 10 other survivors swam 15 hours to reach a nearby island. He towed one injured survivor, engineer Patrick Henry McMahon, by swimming with a strap from McMahon's lifejacket in his teeth.
They later swam to another island where there were coconuts to eat. Kennedy carved a message into one coconut and gave it to a native islander to take to rescuers.
Kennedy later was awarded the Navy and Marine Corps Medal for those actions, as well as the Purple Heart Medal for his injuries. The incident was dramatized in a 1963 movie.
Patrol torpedo boats, such as the PT 109, had mahogany hulls. Plywood was used for the internal structures, chart houses and gun turrets. They were 80 feet long and powered by 12-cylinder gasoline engines.
The boats were used primarily to attack surface ships, but they also were used to lay mines and smoke screens, to rescue downed aviators and to carry out intelligence operations.