He was reacting to publication in newspapers yesterday of transcripts of a recording of a 90-minute conversation at a lunch last Thursday in Mr Fayed's private suite at Harrods. The conversation referred to bribes of pounds 1m or more to ministers.
Mr Rowland, co-chief executive of Lonrho, said of Mr Fayed: 'I thought he understood I was pulling his leg. I was amazed to pick up the papers and find how he had built it up.'
Mr Rowland also offered a theory about why Mr Fayed had allegedly offered the Prime Minister a deal over allegations of wrongdoing by ministers. He said: 'He thought he was in Alexandria doing a deal. He forgot he was in Knightsbridge - that is a slight difference he didn't understand.'
But it was the tape recording of the lunch that upset Mr Rowland, who said it did not take him long to realise it was being recorded.
According to Mr Rowland's account, the joke began with a conversation about a genuine dollars 5m ( pounds 3.75m) payment which Mr Rowland made at the height of the row between Lonrho and the Fayeds over the way they thwarted Mr Rowland's ambitions to take over the Harrods stores group. The payment was made to Chandra Swami, an Indian guru, for tape recordings of a conversation which became the basis of A Hero from Zero, a book published by Mr Rowland as an attack on the Fayeds.
Mr Rowland claimed the swami had introduced Mr Fayed to the Sultan of Brunei. It was through that contact that Mr Fayed played a role in bringing dollars 6bn ( pounds 4bn) of Brunei funds to London at the height of one of Mrs Thatcher's sterling crises.
Mr Rowland said he had then fantasised about the value of a prime minister or a cabinet minister on a scale in which a guru was worth dollars 5m. A prime minister would be worth pounds 100m to pounds 200m, a cabinet minister pounds 5m and a chauffeur a 'couple of quid'.
During the conversation, the subject of payments through banks in Liechtenstein was raised. On the tape, Mr Rowland said he knew quite a few banks but could not remember which he had dealt with.
Next, Mr Fayed suggested that Mr Rowland had paid a cabinet minister pounds 2m. Continuing in the same leg-pulling vein, Mr Rowland said it was pounds 1.5m or pounds 500,000 - he wasn't sure. Mr Rowland took the joke still further, he says, by suggesting that an intermediary could have helped himself to pounds 500,000 along the way, to account for the discrepancy in the figures. Mr Rowland said: 'The whole thing is a joke. I'm sad it backfired. I did resent it when I heard he tape recorded me. I thought: God, the man's up to anything.'
But although he denied the one-year friendship with Mr Fayed was over, Mr Rowland conceded it was strained. He also said: 'We have never paid a penny to anyone employed by government.'