The 58-year-old director was pulled over at about 11.45pm on Friday at a police checkpoint set up for America’s long and boozy Memorial Day weekend. Police had noticed that he was driving erratically.

After paying a $15,000 (£8,220) bond, Mr Stone was released at about 6.30am on Saturday. He said nothing to local reporters who were waiting outside the police department. Police did not identify the drug.

It was not Mr Stone’s first encounter with the police. In 1999 the director was arrested on alcohol and drug charges and, as part of a plea bargain, booked himself into a rehabilitation programme.

Mr Stone’s movies have displayed a strong interest in drugs. Midnight Express, his 1978 screenplay, is a true story of an American jailed in Turkey for trying to smuggle hashish out of the country. He also wrote the screenplay to 1983’s Scarface, about a Cuban émigré who builds a criminal drug empire in Miami while suffering from bouts of ego- mania and paranoia.

Mr Stone also directed the biopic of The Doors, whose lead singer, Jim Morrison, died in a Paris bathtub from a suspected drug overdose in 1971. Even Wall Street, his financial film, included scenes of casual cocaine use.

There has been heightened interest recently in the future plans of Mr Stone, whose career reached its peak in the 1980s with his Best Director Oscars for Platoon and Born on the Fourth of July.

Fed up with the speculation, Mr Stone issued a press release, which said: “Contrary to recent reports in the media, I’ve never announced or intend to make films called Constantine, The Night Watchman or the life story of Margaret Thatcher.”

It went on: “Nor, as also reported, have I fled the United States for France; ‘apologised’ to Turkey for Midnight Express; or denounced my film Alexander, which has now grossed $170 million internationally. Lest my friends are confused, I continue to live in the United States, where I am developing various film projects.”

In an interview, Mr Stone said: “I made a crack that the life of Margaret Thatcher would be great with Meryl Streep.

“It hit the news wires and the internet. Can you imagine me doing the life of Margaret Thatcher?” Mr Stone said that he was baffled by reports that Avi Lerner, the founder of Millennium Films, had announced that the two of them would make a film about Constantine, the Roman emperor, which would be shot in Bulgaria.

“I have never heard of the project,” he said. “I do like Avi Lerner. I faxed him, ‘What are you doing?’ But I haven’t heard back.”

He admitted, however, that the DVD issue of Alexander would tone down the homosexuality featured in the cinema version. “There are a lot of changes, a new third act,” he said of the director’s cut of the film. “We lose 20 minutes and put back in 12. It was a big job.”

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