When Shakespeare’s Globe in London approached him about playing Shylock in “The Merchant of Venice,” Jonathan Pryce didn’t hesitate.

“I said no immediately,” he recalls.

The play and its harsh portrayal of a Venetian Jewish moneylender never appealed to the Welsh-born, Tony-winning actor, whose distinguished career has encompassed “King Lear” in Britain and “Miss Saigon” on Broadway; movies such as “Brazil” and the “Pirates of the Caribbean” series and lately, the HBO television epic “Game of Thrones.”

And then, over a weekend, he looked at the play again, and this time regretted his hasty initial reaction. “Reading it in the world we’re living in now, I had a different response,” he says, conversing amiably in a midtown Manhattan hotel. “You’re in the midst of Brexit and the Trump era — and everything as a result that’s been released.”

He’s speaking, of course, about the racial and ethnic intolerance coursing through national politics on both sides of the Atlantic these days, a state of affairs that audiences can readily relate to in the Globe’s more than respectable “Merchant of Venice” that arrives at the Kennedy Center on Wednesday for a five-performance run in the Eisenhower Theater, ending Saturday. In director Jonathan Munby’s solid, Moorish-inflected production, Pryce heads a cast that includes Rachel Pickup as Portia, the noblewoman who humiliates Shylock in the famous courtroom showdown scene. And just as intriguingly, the actress portraying Jessica, the unhappy daughter who’s suffocating under Shylock’s heavy hand, is the 69-year-old actor’s real-life daughter, recent drama school graduate Phoebe Pryce.

Jonathan Pryce and his daughter Phoebe Pryce as Shylock and Jessica in “The Merchant of Venice.” (Manuel Harlan)

The elder Pryce is the marquee attraction of this touring production, which stopped at New York’s Lincoln Center Festival last week; it will head to Chicago and then China before ultimately finishing up in Venice itself, where the performances are to coincide with the 500th anniversary of the city’s Jewish ghetto. Although Pryce is not Jewish, the part of Shylock seems particularly well-suited to him. Often cast in roles enveloped in an ineffable darkness, he’s a master at embodying that subtlest and most elusive of qualities: the mystery of the heart. Whenever Pryce is involved, there’s an intriguing certainty that his character is fully invested in the secrets he is keeping.

This talent is a huge asset for “The Merchant of Venice.” Shylock’s motivation in sticking to the terms of the loan he’s made to merchant Antonio (here played by Dominic Mafham) — requiring that in the case the debt goes unpaid, a pound of Antonio’s flesh be cut from his body — has been debated endlessly down the centuries. Munby’s “Merchant” underlines the exotic nature of Shylock’s Jewishness in gentile Venice: an improvised scene has father and daughter arguing in Yiddish. More vitally, Pryce’s portrayal grounds Shylock persuasively in a belief that the law applies as sacredly to a Jew as it does to the Christians who spit on him. It may be a misplaced faith, for sure. But this production, more than most, makes clear through its Shylock that the horrific payment he’s seeking is not the real point. It’s the dignity of the persecuted that he’s asserting.

Not every performance in this “Merchant” is quite up to the meticulous standard set by Pryce; there’s a rote aspect to some of the portraits of various Venetian men that renders them hard to keep separate in one’s mind. Still, some other outstanding turns, by the likes for instance of the exuberant Stefan Adegbola as clownish servant Launcelot Gobbo, help reinforce the production’s polished underpinnings. Pickup’s well-spoken Portia makes an elegant impression, even if the heat between her and Dan Fredenburgh’s Bassanio is lacking. Phoebe Pryce, meanwhile, balances her Jessica, after eloping with gentile Lorenzo (Andy Apollo), on an admirable scale of defiance and remorse.

Visually, the production benefits from set and costume designer’s fine architectural and fashion instincts, which atmospherically evoke Venice’s centuries-old access to the cultures and markets of both East and West. This crossroads quality is reflected smartly, too, in the score Jules Maxwell has composed for a band of musicians who roam the stage. (Last week, that was in Lincoln Center’s Rose Theater.)

Pryce, for his part, doesn’t care to give away too much of how he creates a character as complex as Shylock. The Royal Academy of Dramatic Art-trained actor allows that it’s an intuitive process for him, and that he’s not big on research: “That’s why you’ve got a writer,” he says. “If you looked at my script, you’d see that there isn’t a mark in it.” When he’s asked about inspiration, he likes to reply: “I’ve lived for 69 years.”

Earlier in his career, he says, the value of this unvarnished approach was affirmed for him by renowned acting teacher Lee Strasberg, with whom he lunched one day during the Broadway run of “Comedians,” the 1976 play written by Trevor Griffiths and directed by Mike Nichols for which Pryce won his first Tony. (His second was for the role of The Engineer in “Miss Saigon”; his casting as a Eurasian character sparked protests by Asian American actors, but it’s a controversy he doesn’t want to revisit.)

Remembering that lunch, Pryce says: “I said, ‘Mr. Strasberg. I’ve never done a long run in a play before. Do you have any advice?”

Holding a sandwich, Strasberg replied simply: “You do it.” The teacher took a bite, and then added, with a depth of conviction Pryce has never forgotten: “It’s your job.”

Now, he’s passed his love of the job on to his daughter, with whom he is sharing a stage for the first time. But he maintains that when working together, he is able to put aside their family ties. He’s not the proud father of Phoebe up there, he’s the distant, diffident father of Jessica.

“She’s another professional, and I’ve probably said less to her about her performance than I have to the other actors,” he says, adding, though, that reality does have a funny way of intruding. “One day, we did a morning line-run in our street clothes,” Pryce says. “And I suddenly was seeing my daughter again.”

The Merchant of Venice by William Shakespeare. Directed by Jonathan Munby. Sets and costumes, Mike Britton; music, Jules Maxwell; choreography, Lucy Hind; fight direction, Kate Waters; lighting, Oliver Fenwick; sound, Christopher Shutt; music direction, Jeremy Avis. With Dorothea Myer-Bennett. About 2 hours 45 minutes. Tickets, $69-$120. Wednesday through Saturday at the John F. Kennedy Center for the Performing Arts. Visit kennedy-center.org or call 202-467-4600.