Kunis wore an engagement ring on her left hand, but when asked about whether she was set to be married, she turned to Tatum.
"Am I engaged to Channing? Channing and I love each other," Kunis said, smiling.
Tatum - married with a baby - played along: "Yeah, we're not engaged yet, just yet."
"We're getting in that direction though. You know, he has to meet my parents," Kunis said. "That hasn't happened. But one day."
"Yeah, step by step, day by day. I haven't met the crazy Russian family yet," Tatum said. "I'm going to bring a lot of vodka though."
Kunis: "Yes, and cognac - both. ... They like both. They're not picky."
It was the first joint appearance by the co-stars in the summer sci-fi fantasy adventure from the Wachowski siblings Andy and Lana, creators of "The Matrix" trilogy. Observers have compared the film to a mashup of "The Fifth Element" and the Snow White fairy tale based on early trailers. Tatum said he didn't agree.
"It's really, truly their own imagined sort of world and the circumstance that happens in the world. People always say that they're tired of seeing old movies remade and like comic book movies made. This is a completely out of the Wachowskis' brain type of a crazy film. So yeah, it's its own thing, for sure," he said.
Tatum plays Caine, a genetically engineered part-wolf hunter who tracks down and helps Kunis' character, Jupiter - a humble woman who finds out she's marked as a leader of cosmic proportions.
"It was the most challenging role I've ever had, physically speaking. Because you had to endure seven months of physical training and sustain it," Kunis said. "And test yourself and kind of test your patience with things. Because you get - I know you did for sure - you get frustrated with yourself when you can't do certain things."
Tatum, 33, said he took a "leap of faith" in playing the role "because so much of it is not known - like you have to take the movie not knowing I would say 89 percent of what you're going to be asked to do because it's a completely made up (world)."
He added: "I'm a genetically engineered human and wolf or what would be a wolf. I don't know what that's going to look like. I'm just assuming that we're going to get to somewhere cool."
Kunis, 30, added: "There are no rules in this world. So there's no right or wrong. ... You have no guidelines to go by, which kind of makes it fun but makes it also very stressful."
"Jupiter Ascending" is set for release July 18.
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