Bill Murray as Franklin D. Roosevelt in a scene from “Hyde Park on Hudson.” (Nicola Dove/AP)

A long time ago, there was a restaurant in New York called Asti, where the waiters sang opera while they served up plates of pasta underneath signed photographs of Babe Ruth and Noel Coward and where, on at least one occasion, Bill Murray led customers — including this writer, who happened to be dining with one of Murray’s friends — in a conga line through the restaurant, out to 12th Street and back in again.

At the Toronto International Film Festival in September, Murray brightened when a visitor reminded him that they’d met before. “Were you there the night we were with what’s-his-name, Sergio Leone?” he says, his voice rising excitedly, “and we tried to stick [him] with the bill?”

Er, no — different table. But the Asti story is just one of hundreds that abound about Murray, who since breaking out on “Saturday Night Live” and becoming a star in such comedies as “Ghostbusters,” “Groundhog Day” and “Caddyshack,” has pursued something of a dual career, cultivating an inscrutably appealing on-screen persona in indie films by the likes of Sofia Coppola, Jim Jarmusch and Wes Anderson, while making himself almost alarmingly accessible off-screen, crashing a group of friends’ kickball game on Roosevelt Island one day and showing up at a college baseball game the next. The Murray legend, by now, is well known: He doesn’t have an agent, or a manager or a publicist, and takes movie offers only by way of calls to an 800-number that he rarely checks; according to one strain of the myth, he’s been known to approach strangers from behind, cup his hands over their eyes and say, “Guess who?” (When they turn to discover that it’s Bill Murray, he reportedly says, “No one will ever believe you.”)

It’s precisely this puncturing of movie-star remove, this combination of ubiquity and elusiveness, this refusal to hew to the conventions and tribal rituals of celebrity, that has endeared Murray to his fans over his 35-year career, earning him a store of goodwill that turns out to be crucial to his latest project. In “Hyde Park on Hudson,” Murray plays Franklin D. Roosevelt, who, like Murray, enjoyed the almost worshipful affection of the American public. In the film, Roosevelt entertains England’s King George VI as the monarch seeks the United States’ support for Britain in its fight against Hitler.

But “Hyde Park on Hudson” also presents a more unsettling portrait of Roosevelt, who, when he’s not secretly tippling with the king, can be seen carrying on an affair with his distant cousin, Daisy Suckley (Laura Linney) — a relationship that, the film suggests, was just one of many such dalliances in which Roosevelt maintained a balance of disarming sincerity and ma­nipu­la­tion.

Bill Murray attends the 2012 Toronto Film Festival to promote “Hyde Park on Hudson.” (Chris Pizzello/Invision/AP)

Murray says he related to what he saw as Roosevelt’s compartmentalization, as well as his shrewd deployment of native charisma. “When I was doing it, it came from a major highway in here,” he says, pointing to his chest. “Some of that stuff was coming right down the interstate. It was like, whoosh. Because I can do that. I’ve got that weapon, or that tool. I can do that at 90 miles an hour, I can do that at 115.”

For director Roger Michell, the unsavory aspects of story demanded an actor with Murray’s ingratiating brand of charisma. “The only actor I could see making the film work was Bill,” Michell said at the festival. “Because there’s something forgivable about Bill. There’s something mischievous about Bill. There’s something ineffably charming about Bill.”

“Roger said to me, ‘If you don’t do it, I’m not going to do the movie,’ ” Murray recalls. “They always say that, but I could see why I was a good call for this one. You like to get ones like that, where you go, ‘Holy cow, I can kill this one. I can kill this thing.’ ”

If Murray playing Roosevelt feels like natural casting, both physically and psychologically, “Hyde Park on Hudson” represents something of a departure for the actor, who lately has focused on small but toothsome roles in films such as “Get Low” and summer’s art-house hit “Moonrise Kingdom.” When he read the “Hyde Park on Hudson” script, he says: “I knew I had to do it. There was something in me at the time saying [that] I had to be more ambitious. Because I don’t really feel like I have any ambition or drive. . . . I’m not really a hustler, or anything like that.”

But isn’t it that lack of careerism that has worked so well for Murray over the years?

“It has worked for me,” Murray says. “It’s extremely powerful to say no; it’s really the most powerful thing to say.” He credits his laidback approach to his earliest days performing at Chicago’s Second City, where he watched the likes of John Belushi, Dan Aykroyd and Gilda Radner precede him into what he calls “the explosion” of instant fame on “Saturday Night Live.”

“It was a little more of a tougher place, maybe, a little more of an educational place, than it is now,” he says of Second City, “where you really had an education in how you comport yourself, how you make a career and what informs your choices.” Of his fellow Second City alums, he recalls, “You watch as they slam against the walls and who keeps going forward and what it is that keeps them going.

“The things that I learned, I just kept rolling with, and saying no is a big, big part of it,” he continues. “I try never to be desperate for a job. . . . I don’t even go looking for work and the good stuff comes to me. Better stuff comes to me than I ever got [when] I had agents throwing junk at me. It’s just sweet. It’s swell.”

Murray will next star in “A Glimpse Inside the Mind of Charles Swan III,” by Roman Coppola, as well as Anderson’s “The Grand Budapest Hotel” and the World War II heist drama “The Monuments Men,” directed by George Clooney. “I envy people like Clooney. God, he works so hard,” Murray says wistfully. “He’s working all the time. But he doesn’t have a wife, you know? He doesn’t have kids. If I didn’t, that’s just what I’d do, because it really is fun.” (Murray has six children and was divorced from his second wife in 2008.)

“People like George and myself, we really like the doing of it,” Murray explains. “So my challenge is to try to live as well when I’m not working as when I’m working. . . . I’m much more of a whole person when I’m working. I’m more collected, I’m more connected, I’m more there.”

Murray has to go get ready for the splashy “Hyde Park on Hudson” premiere in a few hours, where he’ll once again beguile the assembled fans and press with that trademark ineffable charm. Still, even warmth as spontaneous and offhanded as Murray’s comes with its share of shadow material.

“When you’re a public person and you choose to be more private, you’re constantly in shadows,” Murray says before heading out. “When you go out there, you’re on your best behavior, in a way. You’re kind of leaning forward, leaning into it and engaging.” He contrasts that with those times when he’s reluctant even to face the day.

“That’s why I feel better when I’m working,” Murray explains. “Because I have to be. There’s real proof of whether I am nor not. . . . When you make the day, you can look around and everyone knows whether you were or you weren’t. You are, or you’re not. That’s why I have to be at hours at a time, even if they’re only minutes at a time, and not get too gone for long periods.”

Hyde Park on Hudson

95 minutes, opening at area theaters on Dec. 14, is rated R for sexual content.