The new NBC drama is based on the ITV series of the same name, which starred Helen Mirren and ran from 1991 to 2006.
Griffin told Xfinity: "I actually was familiar with it, and I was a huge fan of the original. The amazing thing was sort of watching the evolution of [Mirren's] character, and I remember that it was something that I found really inspiring."
Griffin, who plays Detective Augie Blando in the NBC version, explained that the remake will use "some of the devices" featured in the UK series.
"But [the writers] find ways to twist it," he said. "Even if you recognise that it comes from the original, they turn it on its ear so you don't see what's coming."
He continued: "They're probably the most talented script-writing team I've ever seen. These guys had 13 episodes before other shows had even [story]boarded one."
Prime Suspect's executive producer Alexandra Cunningham previously insisted that the remake will diverge from the original show.
Lynda La Plante, creator of the UK series, has also reportedly expressed her approval of NBC's version.
Prime Suspect continues tonight at 10/9c on NBC.
> Friday Night Lights exec to guest star in Prime Suspect
Watch a preview video for NBC's Prime Suspect below: