Tom Cruise Premieres Edge of Tomorrow in Three Countries in 24 Hours
updated 05/29/2014 AT 06:30 AM EDT
•originally published 05/28/2014 AT 12:45 PM EDT
Speaking in London at the 6:30 a.m. start of a red carpet odyssey that will also see him promote his latest sci-fi action film, Edge of Tomorrow, in Paris and New York within a 24-hour period, Cruise laughingly agreed that the idea was just as wild as fighting the horde of demented aliens he encounters in the movie.
"I think they're equal!" Tom joked to PEOPLE at the BFI IMAX, near London’s Waterloo Station, before adding that filming in the British capital also came with its own problems – albeit of a different kind.
"I loved landing a helicopter in Trafalgar Square," he told reporters. "It is something I have always wanted to do ... I didn't fly it but I was in the back and it was amazing. It was a blast."
Perhaps too much fun: "The first takes we did, I came out of the helicopter and I was smiling," he continued. "But that's not the character. So we had to do a few takes there. It was a lot of fun."
Cruise's costar, new mom Emily Blunt, who looked trim in a strapless Osmond gown, says Cruise is "so fearless that he's almost fearful of being fearless."
Something else he might be fearful of? Being late. The superstar was expected at the red carpet in Paris at 2 p.m. local time but was delayed getting out of London. After that he was set fly to New York, where his final red carpet and screening took place at 10 p.m. ET.
Edge of Tomorrow follows Major William Cage (Cruise) who is stuck in a time loop and must re-live the same day of combat over and over as he fights alien invaders.
At his second red carpet in Paris, Cruise told PEOPLE, "I'm beginning to feel like Cage."
Check out the premieres of Edge of Tomorrow below: