Cavill stars in the movie as a man whose family is kidnapped while they are on holiday.
Discussing the film, Cavill revealed that he was thoroughly impressed with Weaver.
"I've got to say, Sigourney Weaver was fantastic. I really enjoyed working with her; she's a wonderful woman and a fantastic actress," the actor said, reports Flicks and Bits.
He then joked: "Being her target, as much as it was horrifying and scary in the moment, it was a pleasure at the same time. Ripley hunting me down!"
Cavill also discussed working with Willis, who plays his character's father in the action thriller.
"With Bruce Willis, in a movie like this, having someone like him with his immense action-figure status is fantastic – especially with the way the story goes," he said. "You almost expect The Cold Light of Day to go in a [Die Hard] John McClain direction for a second, you see an inkling of it, and then all of a sudden it's gone."
Cavill further explained: "With [my character] Will's call to action, it's in his genes, his father is made of that kind of stock. Will is his son after all, if not by personality, then definitely by blood.
"There are moments in the story where Will's level head and sense of attack – as opposed to flee – really kick in. Bruce Willis was great."
The Cold Light of Day opened earlier this year in the UK and debuts in US cinemas on September 7.
Cavill also plays Superman in the upcoming Man of Steel, which opens in 2013.
Watch Henry Cavill discuss The Cold Light of Day below: