Michelle Williams channels Marilyn Monroe

Her eyes were searching the grounds of the Beverly Hills Hotel, peeking over the bougainvillea at a row of terra cotta-roofed buildings.

“I always wonder which bungalow was hers,” said Michelle Williams, staring into the distance at a lodging that could have been home to Marilyn Monroe. The icon, whom Williams plays in the film “My Week With Marilyn,” lived at the hotel in the late 1950s while in production on the movie “Let’s Make Love.”

“Is it too pretentious to say I feel I have a relationship with her?” the actress said suddenly, as if she could feel the blond’s spirit. “The more time I spend with her, the closer I feel to her.”

On the surface, Williams, 31, doesn’t seem to share much in common with the tragic star. Monroe was all curves and soft flesh; Williams is pixie-like – on a recent fall night, she was covered up in black slacks and a sweater with a Peter Pan collar. Monroe affected a ditsy persona that many critics abhorred, and she was never nominated for an Academy Award; Williams, a two-time Oscar nominee, quotes the likes of Gustave Flaubert and Walt Whitman. The late actress was beholden to the studio system; Williams often opts for determinedly noncommercial, independent films such as the minimal “Meek’s Cutoff” or the emotionally raw “Blue Valentine.”

Still, on the set of “My Week With Marilyn” – which opens in Los Angeles on Wednesday – Williams felt an inexplicable connection to Monroe. During the shoot, she found meaning in seemingly ridiculous things – like an article in the National Enquirer.

“There was a story about a psychic who had come into contact with Marilyn, and she said Marilyn approved of what I was doing. That took on a lot of meaning for me,” she admitted. “Maybe it was Marilyn, but I felt more fragile than I usually do on this movie. I felt more dependent on other people’s kindnesses. I would live off a compliment that the camera man gave me for two weeks. It would feed me. It would get me out of bed.”

“My Week With Marilyn” is drawn from two memoirs by Colin Clark, who was an on-set “gofer” during the 1956 production of “The Prince and the Showgirl.” Berated by her costar and director Sir Laurence Olivier and facing the dissolution of her marriage with Arthur Miller, Monroe reportedly sought refuge in a quasi-romantic relationship with Clark, nearly a decade her junior.

While Monroe wore her vulnerability openly, Williams has long appeared outwardly resilient, even as she has faced difficulties as challenging as those Monroe experienced. At 15, the Montana native struck out on her own, legally emancipating herself from her parents and moving to Los Angeles to pursue acting. At 25, she and her “Brokeback Mountain” costar Heath Ledger became parents to a daughter. Ledger died of an accidental drug overdose three years later, and Williams has raised their child, Matilda, as a single mother.

After his death, Williams struggled to find her footing in Hollywood. She took a year off, she said, “unsure of how I would go back, or if I wanted to go back” to acting. After she began to emerge from the fog of grief, she recommitted herself to the craft and decided to take a more gut-driven approach to her career.

“I read this Flaubert quote once that I really love: ‘I want to live the quiet life of the bourgeois so that I can be violent and unrestrained in my work,” she said, reciting the words from memory. “And I like that. Live the simple life and save all your extra forces for your work.”

When she read the script for “My Week With Marilyn,” adapted for the screen by Adrian Hodges, Williams instantly felt compelled to do the movie. Growing up, her room had been filled with images of Monroe: a cardboard cutout and a poster of her running through a field, arms outstretched, joyous.

“I remember thinking that if even a woman that beautiful clearly has trouble and is damaged and has insecurities, then we’re all entitled,” said Williams, who was born 18 years after Monroe died.

When director Simon Curtis visited her home in upstate New York two years ago to talk about the role before she’d officially signed on, he left a picture of Monroe in Williams’ home — a small photo underneath a telephone.

“I kept staring at her face every day in my kitchen thinking, ‘Can I really?’” the actress said. “With any sort of part that I take, there’s a hint of an idea of how I’m gonna do it. I don’t really know the full scope of it, but there’s something inside of me gravitating towards it.”

To figure out who Monroe — “this stranger” — was in the months leading to filming, Williams spent hours practicing Monroe’s vocal cadences in her house while Matilda was at school. She’d teeter around in high heels, tying a belt around her knees to experiment with how to achieve Monroe’s famous wiggle.

“The biggest discovery I made was that Marilyn Monroe was a character she played,” said Williams, explaining she reached that conclusion through reading Monroe’s own writing as well as accounts by photographer Eve Arnold. “So I lived with her, and I never stopped trying to find more information. Even on set, on the 10-minute breaks, I would be back poring through photos or with my earphones in watching a movie. I was obsessed. I was on the trail of something. There were clues, and I had to solve a mystery.”

Harvey Weinstein, whose company is releasing the film, said he was impressed at the level of Williams’ preparation, how she could quote passages from Maurice Zolotow’s biography on Monroe.

“Michelle researches a role like no one I’ve ever encountered,” Weinstein wrote in an email. “She watched and studied the movies and photos; she read every book, every biography.… She could describe how Marilyn wiggled and winked while quoting some of her best lines, [like] when she teased that she was nude by saying, ‘I have nothing on but the radio.’”

Director Curtis decided to shoot “My Week With Marilyn” at Pinewood Studios, where “The Prince and the Showgirl” was filmed more than 50 years ago. Both actresses were 30 when they were on the film stage just outside London.

During filming, Curtis said, he noticed Williams’ delicateness, so he tried to give her additional time and space for her process.

“I wanted to give her as many takes as I could, because there’s something about creating this performance — you never quite knew when Marilyn would pop,” said the filmmaker, who would sometimes do 12 takes of a scene with the actress. “I just felt she needed and deserved tremendous support, and I hope — unlike Marilyn — she got it.”

Williams’ performance has already generated lead-actress buzz for the Academy Awards. (Her previous nominations came for her supporting turn in 2005’s “Brokeback Mountain” and her leading role in last year’s “Blue Valentine.”)

Don Murray, who costarred with Monroe in “Bus Stop” — which she shot immediately before “The Prince and the Showgirl” — said he didn’t find one false note in Williams’ interpretation of the legendary actress.

“Those who have worked with Marilyn say ‘Bus Stop’ was her best-behaved film, but she was still two or three hours late and also had trouble remembering her lines. The littlest thing would disturb her and send her concentration flying,” recounted Murray, 82. “I was astonished at how Michelle captured that. She got that total confusion — almost falling apart emotionally. Marilyn suffered every little thing.”

Williams — in production on Sam Raimi’s “Wizard of Oz” prequel — said “My Week With Marilyn” helped her to finally grow up. It was both the biggest challenge she’s ever taken on and the most fulfilling, she added, because it helped her to accept herself.

“I think I became an adult making this movie. I’ve always been scared of myself somehow. Or apologetic or something,” she said quietly. “I just felt for a long time that I was grappling with something I couldn’t quite master or understand. But I’ve been a parent for six years now. I have an amazing daughter, and at some point in the last year, it dawned on me that has to have something to do with me. And I need to give myself a break.”

amy.kaufman@latimes.com