Fayed said that he did not want to cause any further pain to Diana's sons, The Times of London reported.
"I'm leaving the rest for God to get my revenge," he said.
Fayed has argued that the 1997 crash in Paris that killed his son, Dodi, and the princess was engineered by British intelligence agents working for the royal family. But a French investigation and this week a British coroner's inquest blamed the crash on the driver, who also died in the crash, and photographers pursuing Diana.
Wednesday, the Metropolitan Police in Britain announced an investigation into the testimony during the inquest of Diana's butler, Paul Burrell. A police spokesman said that a complaint had been made about possible perjury.