After meeting Denzel Washington in Paris I read this quote from Clifton Fadiman, the late American intellectual, journalist and broadcaster:

"The man who looks you straight in the eye, particularly if he adds a firm handshake, is hiding something." It seems pertinent since 24 hours earlier Washington, the two-time Oscar winner, arrived at our rendezvous dressed entirely in black, looked me in the eye and shook my hand firmly. His reputation as an intensely private man, I will conclude in the aftermath, is not undeserved.

Professionally, he buries himself in the myriad characters he has brought to the screen across the last quarter-century. We have seen him winning an Oscar while fighting for the north in the Civil War and then almost winning again while agitating for human rights, as Malcolm X. He has gone on to be a gangster, an accused boxer, a corrupt cop, an escaped slave and a sozzled airline pilot. There have been some duds but his percentage is comparatively low.

Study the A-listers who began to dominate during the 1990s - Mel Gibson, Julia Roberts, Harrison Ford, Tom Cruise - and Washington is the only one whose credibility remains unsullied. He is a marvel, the most famous African-American actor since Sidney Poitier and a friend of the Academy Of Motion Picture Arts and Sciences; they have nominated him no fewer than six times. He has appeared in countless magazines and charmed dozens of talk-show hosts and yet he remains a man of mystery, his own personality obscured.

"I do not see myself as a movie star or a celebrity," says the 59-year-old. "I am a working actor." If ever he has had a mantra, this is it. His longevity owes much to his ability to maintain a private life. He is still married to Pauletta Pearson, whom he met on the set of the television film Wilma in 1977 and married in 1983; his four children are all successful in their fields and he occupies few column inches in the tabloid archives. "I just want to do the work," he adds.

His most recent piece of work is The Equalizer, a vigilante movie that borrows its central conceit from the 1980s television show of the same name, which made Edward Woodward a household name on both sides of the Atlantic. The film comes to the screen courtesy of Antoine Fuqua, who directed Washington to his second Oscar victory with Training Day in 2001.

Washington plays a reluctant vigilante but he is a killer nonetheless and in many ways it is an unlikely choice, even though it was developed as a movie specifically for him. With a few notable exceptions, like Man On Fire, he has mostly avoided violence on screen. When playing a black-hearted, drug-addled cop in Training Day, he insisted the character get his comeuppance.

Washington is a devout Christian and reads the Bible daily (he is currently on the Book Of Daniel). I wonder, then, if the violence he perpetrates on screen in The Equalizer makes him uncomfortable? He looks at me steadily, holding my gaze. "It could," comes his eventual reply, "but then the Bible is violent. Certainly Abel might think so."

He flashes a smile. I ask the question again. He smiles again. "I think that is something the character is struggling with," he says, before adding: "I don't agree that someone should become the judge and jury, but it's a movie." So it wasn't fun to make? "I don't know. When you are making it and you are doing 20 takes over and over and over, I would not call it fun. No, I would not use the word 'fun'."

Washington did not watch the original television series with any regularity and says he didn't catch up with it before making the film. There was no need; only the central conceit and the name of the character, Robert McCall, carry from one to the other. "I didn't watch it because I didn't want to be influenced," he says. "If there was an idea I had and then they had done it on the show then you go, 'Oh, I can't do that.' I didn't want to get into what I can't do. And right at the beginning, the producers said they had taken the title and the basic premise, not the specifics."

That basic premise is that McCall is a man with a shady past - in the film, he is a former black ops commando - who works at a DIY superstore and lives a simple life, helping his co-workers and sitting at home alone. He has insomnia and frequents a local cafe late each night, where he befriends a young prostitute, played by Chloe Grace Moretz.

When her Russian pimps beat her up, McCall tries to pay them off. When they refuse his offer he kills them all in a 16-second whirlwind of violence. A shot-glass and a corkscrew are among the tools he employs. McCall is a piece of work. "There is one scene later on with a drill and my wife started covering her face," he says, "but you don't see anything .You just think you do."

After the first act of violence, things remain relatively restrained until a final showdown. "It is manipulation and that is the movie experience. When I first saw Hitchcock's The Birds you couldn't tell me they weren't for real. I went outside and was expecting birds to peck out my eyes."

Thankfully for Washington this did not come to pass - his eyes are very much intact and make frequent contact with mine throughout the interview. They are bright and the man is too; charming, beguiling even, and often talking in anecdotes. Ever elusive, he prefers a yarn to a direct reply. He is a born storyteller, it seems.

At one point I ask him whether he empathises with the Equalizer's need to find justice. "I remember working on Training Day. I went out with a police officer and he got a call from someone's wife saying her husband has got a shotgun and she is scared," he says. "We drove past the house, did a U-turn and then we were facing the house. The officer told me to wait in the car and he walked towards the house.

"Then a car came screeching up. Now, he could have panicked or taken his gun out. In fact, it was the guy's daughter. But the cop still went up and faced it all and defused the situation and he could have been shot. He had to make a split-second decision but he could have got his head blown off. It is easy to complain about what those guys do."

It was Training Day that first united him with his director on The Equalizer, and the pair are due to unite for a third time next year when they take on a remake of The Magnificent Seven. Fuqua has cast Washington in the Yul Brynner role, which was originally earmarked for Tom Cruise.

Washington says: " I brought Antoine The Equalizer script and he brought me The Magnificent Seven. I said, 'Wow.' I've never done a western." Have they discussed any story changes? "Antoine hasn't talked so much about The Magnificent Seven. He talks more about the film that helped him decide to become a filmmaker, which was Seven Samurai." The Magnificent Seven was based on Akira Kurosawa's 1954 film. "So if you want to call it a remake, it is a remake of Seven Samurai."

It is an intriguing thought, but then Washington is an intriguing character. He grew up a keen sportsman and dreamed of a career in American football - a dream his son John David fulfilled by playing in the NFL. Acting was not on Washington's horizon. "I have never had movie star ambitions," he says, "and who was I supposed to look up to anyway? Not many movie stars looked like me, except Richard Pryor. No, that wasn't my dream."

Instead, he went to Fordham University in New York to study journalism but strayed from his studies as the good times rolled. These were the heady days of the 1970s and Washington was suddenly flunking. The college was all set to kick him out when his epiphany came. It was March 27, 1975, and a 20-year-old Washington was sitting in his mother Lynne's beauty parlour in his hometown of Mount Vernon, New York.

"There was a woman sitting there and she had a prophecy," he says, spinning another intriguing if well-worn tale. "She prophesied I would travel the world and speak to millions of people." At the time the prophecy suggested a life in the ministry of God more than guaranteed success in the film business, but he went to a camp that summer as a counsellor and performed in a stage show. "Everybody was saying I was a natural," he recalls.

Washington enjoyed it so much that in the autumn term, when he returned to college, he switched the focus of his studies to theatre. Not long afterwards he landed the leading role in a version of Eugene O'Neill's The Emperor Jones.

Thus was his acting career born, and the prophecy started to take shape. Washington's screen career began with television and he became one of a handful of African-Americans to appear in the hospital drama St Elsewhere before he moved to the big screen and earned the first of his six Academy Award nominations for 1987's Cry Freedom, directed by the late Sir Richard Attenborough.

He won the Oscar for Best Supporting Actor on the back of 1989's Glory and became a household name in the 1990s with powerhouse performances in the likes of Malcolm X, The Pelican Brief, Philadelphia, Crimson Tide, The Bone Collector and Courage Under Fire. In 2002 he won the Best Actor Oscar for his corrupt policeman in Training Day and he was nominated for a sixth Oscar in 2013 after his starring role as an alcoholic commercial pilot in Flight.

"Flight was a rich dramatic role and that was only about a year ago, but tastes have changed and the industry has changed," he says. "What used to be independent companies are now owned by really big ones. They have stockholders so look for the more profitable stories and sequels and the like.

"And this summer was actually a good indication that it doesn't always work. It was a weak summer for box office. Just because something is a sequel doesn't mean it'll be successful. In fact the highest grossing film of the summer, Guardians Of The Galaxy, wasn't a sequel."

Washington regards the 1970s as the heyday of filmmaking. He loved Al Pacino and Robert De Niro in The Godfather films and the latter in Taxi Driver. "It'd be interesting to look back and see what the early blockbusters were as opposed to what they are now," he says. "Would Forrest Gump, for example, be successful now? I don't know. I don't want to say things got lazier but they are going with what they think is the safest option."

He has directed two features - Antwone Fisher (2002) and The Great Debaters (2007) - and starred in both. He plans to direct again soon but won't be drawn any further. Would he return to TV, I ask? "I haven't been asked," he says, "so I can't tell you that. But a good story is a good story."

As I rise to leave he shakes my hand once more and looks me straight in the eye. n

The Equalizer (15) is in cinemas from Friday.