'Many Saints of Newark' 's Alessandro Nivola Felt 'Familial Affection' for Costar Michael Gandolfini

Alessandro Nivola became fast friends with costar Michael Gandolfini.

The 49-year-old actor stars as crime boss Dickie Moltisanti in the new film The Many Saints of Newark, a prequel to the hit television series The Sopranos. For the movie, Michael, 22, takes over his late father James Gandolfini's iconic role as a younger Tony Soprano.

"We started meeting up once a week at Junior's cafe in Downtown Brooklyn for lunch and, you know, shoot the s―. By the time we were filming, we had spent a lot of time together," Nivola told PEOPLE during a conversation at the U.S. Open last month about developing a mentorship dynamic with Michael prior to production.

"I think we were both dealing with the pressure of the job," he added, "because he was taking on this iconic role that his father had played, and I was taking on the role of a lifetime after 25 years of acting in movies and never having had this kind of an opportunity."

"So we kind of bonded over the weight of that. I really felt a kind of familial affection for him," said Nivola.

He explained, "It was very important that we had that easy rapport because [writer] David Chase is very unsentimental, and the scenes need to convey that kind of love between us without us ever talking about it. It was important that it was just there."

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Through channeling the character of Tony Soprano, Michael said he was able to connect with his dad, who died at age 51 of a heart attack in 2013, in a new way. He tells PEOPLE in this week's issue, "I feel a bond. I understand the toll that he went through, the hard work that he put in as an actor that maybe I wouldn't have known as a kid. I respect him as an actor more."

RELATED VIDEO: James Gandolfini's Son Michael on Playing Young Tony Soprano and Developing His 'Physicality'

No matter what, "my dad is always going to be my best friend," Michael notes. "He's always just going to be my dad to me."

The actor adds that he can't wait for audiences to see him as the character his dad made famous. "This moment means so much more to me in many ways. It means a lot to my family," he shares. "It's been a long time coming and I'm just so honored."

The Many Saints of Newark is now playing in theaters and streaming on HBO Max.

For more on Michael Gandolfini, pick up the latest issue of PEOPLE, on newsstands now, or subscribe here.