His mother, Evelyn Worthington, a former Texas school teacher who lives in Houston, "has never met John F. Kennedy nor any other member of the Kennedy family," according to the statement issued by the family today.
Vanity Fair posted a lengthy article about Worthington's claims on its Web site today, reporting that its analysis of JFK hair strands supported "non-paternity."
The article, by David Friend, recounts how Worthington approached the magazine through an attorney in 2006 who said Worthington, 46, was prepared to change his last name to Kennedy and name his newborn child John F. Kennedy III.
In an interview with ABC News, Worthington said his relationship with his mother was strained and that he did not know details of how or when she would have been with the president.
Worthington was born Nov. 22, 1961, indicating he would have been conceived in the first month Kennedy took office.
White House appointment records reviewed by ABC News indicate President Kennedy was not in Texas at any point in January or February 1961 and, indeed, rarely left Washington, D.C.
As to the coincidence of his birth date matching the day on which Kennedy was assassinated two years later, Worthington said, "It was disturbing."
Worthington said his family had close connections to Lyndon Baines Johnson who he speculated may have introduced his mother to Kennedy.
"It would make sense that there would be a connection there," Worthington told ABC News.
According to the family statement, "Mary Evelyn Worthington has never met Lyndon B. Johnson. Jack R. Worthington, Jr. is the natural born son of Jack R. Worthington, Sr. and Mary Evelyn Worthington."
Worthington said his mother has changed her story for the public.
"If her statement is true then I have the congenital disease my father died from and my children have a 50 percent chance of having it," he said. "I just don't believe my mother is that cruel or stupid to have misrepresented my parentage."
Worthington added that he was extremely disappointed by the Vanity Fair article, calling it a "hack job."