Al Fayed, who has been Fulham's chairman for 14 years and invested millions of his own personal fortune in the club, called Hughes "a strange man" who was in danger of becoming "a forgotten man" until Al Fayed rescued him last year.
Hughes, 47, was Fulham's manager from July 2010 until he quit after the end of the season saying: "as a young, ambitious manager I wish to move on to further my experiences".
The former Manchester City and Wales national boss reiterated that stance on Saturday when he was quoted in the British media as saying: "I felt my ambition for where I wanted to take the club was not matched.
"Historically Fulham was a club that was happy to be in the Premier League and that was their ambition, but it was not my ambition for them.
"In conversations they were saying: 'We know exactly what you're about Mark, but really we are just happy to stay in the Premier League'"
Those remarks brought a sharp response from Al Fayed in an open letter on Fulham's website (www.fulhamfc.com).
It began: "What a strange man Mark Hughes is. Sacked by Manchester City, he was becoming a forgotten man when I rescued him to become manager of Fulham Football Club."
Al Fayed, at 82 no stranger to public spats and controversy, continued: "Even when results were bad, I did not put pressure on him. I gave him every support -- financial, moral and personal.
"He fully negotiated a two-year extension to his contract. On the day he was due to sign, he walked out without the courtesy of a proper explanation.
"And now he insults the club, saying it lacks ambition, and the players who delivered an eighth position finish last season and a place in the Europa League.
"He is not just disrespectful but entirely wrong. Fulham has just announced plans for a splendid new riverside stand that will substantially increase the capacity of Craven Cottage.
"In every aspect of its work, Fulham is a progressive club with a top manager in Martin Jol, the man we had really wanted when Hughes was appointed.
"We shall endeavour to prosper without him simply because, when the challenge came, it was not the Club but Mark Hughes who lacked the courage and ambition to take on the task of leadership.
"If people are looking for a flop, they only have to go no further than the man who has lost his spark."
Former Manchester United striker Hughes, nicknamed Sparky, was not immediately available for comment.
Fulham were beaten 3-1 at the Cottage by Everton on Sunday and are 17th in the Premier League, one place and one point above the relegation zone after nine matches in the 38-game season.