Johnny Depp gave the popcorn-shaped award to two of the film’s stars, Josh Hutcherson and Sam Claflin.
Jonah Hill won best comedic performance for The Wolf of Wall Street.
Jared Leto presented Mila Kunis with the best villain prize, while Channing Tatum won the trailblazer award.
Josh Hutcherson remembered his late fellow cast member Philip Seymour Hoffman, who died earlier this year of a drug overdose, and said: “I know that if Philip were here, he would think this is really cool.”
Hunger Games: Catching Fire – a young adult film about an oppressed society fighting back – has earned more than $850 million globally and was the second-biggest US opening of last year, behind Iron Man 3.
The final part of the story, Mockingjay, has been split into two films that will be released in 2014 and 2015 respectively. The movies are based on Suzanne Collins’ hugely successful dystopian fantasy novels.
Mila Kunis won for her performance in Oz the Great and Powerful, Sam Raimi’s fantasy film which pays homage to The Wizard of Oz while Channing Tatum, star of 22 Jump Street and Jupiter Ascending, was the first male winner of the trailblazer prize, after Emma Stone and Emma Watson.
Favorite character of the year was a surprise win for Shailene Woodley, who played Tris in Divergent, beating Jennifer Lawrence’s Katniss in The Hunger Games. They each received more than 9 million votes.
The Fast and the Furious actress Jordana Brewster introduced a special tribute to the film’s late star Paul Walker, who died in a car crash last November. He won the MTV movie award for breakthrough male performance in 2002.
Co-star Vin Diesel added in a video clip: “I’m always going to be here for you even when you tell me to go. That’s who Paul Walker was.”
Mark Wahlberg, star of The Fighter and the upcoming Transformers film, collected the generation award.
“Many people have gotten this award before. Jim Carrey, Adam Sandler, Ben Stiller, Jennifer Aniston… and you know what they all have in common? They’re all old. This is the too old to come back award,” said Mark Wahlberg.
Rihanna won the prize for best cameo performance in the comedy This is the End and she later performed The Monster with Eminem.
Ellie Goulding sang Beating Heart, from the soundtrack of young adult thriller Divergent.
The MTV ceremony also recognizes some non-traditional categories: Zac Efron won best shirtless performance, while best kiss went to Emma Roberts, Jennifer Aniston and Will Poulter for a scene in their road-trip comedy We’re the Millers.
The awards are also an opportunity for the film industry to showcase upcoming summer films and their stars.
Andrew Garfield, Emma Stone and Jamie Foxx from The Amazing Spider-Man 2 introduced a clip of their new film, featuring Garfield’s Spider-Man encountering the blue villain Electro (Foxx) in New York’s Times Square.
Ellen Page, one of the stars of X-Men: Days of Future Past, presented a clip from the forthcoming blockbuster, in which the X-Men join forces with their younger selves.
Aaron Taylor-Johnson, who is starring in Godzilla, gave Orlando Bloom the award for best fight, for a sequence in The Hobbit: The Desolation of Smaug, where Bloom and co-star Evangeline Lilly took on the brutal Orcs.
MTV Movie Awards 2014 were hosted by TV presenter, comedian and writer Conan O’Brien.
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