The petition, carrying more than 36,000 signatures garnered online, was presented two days before Sunday's Academy Awards at its Beverly Hills headquarters by Arab-American peace activist Nonie Darwish.
Darwish said Paradise Now "did not show the evils of terrorism enough".
"Any one of us could be a victim of terror at any time," she said. "Islamic terror has become an epidemic. We don't need to understand it. We don't need to excuse it ... . No more. We need to end it."
John Pavlik, Academy spokesman, declined to comment on the petition and said he was unsure whether officials would examine it.
However, he was clear about whether the nomination of Paradise Now would be withdrawn. "Not gonna happen," Pavlik said.
"It would be physically impossible to happen between now and Sunday and, beyond that, we're not going to disqualify films because some people don't like the content."
Paradise Now tells the fictional story of two young mechanics from the West Bank town of Nablus sent to carry out a double suicide bombing in Tel Aviv.
The film won a Golden Globe Award in January and is nominated for an Oscar for best foreign film.
The petition campaign was organised by Yossi Zur, an Israeli whose 16-year-old son, Asaf, died in a bus bombing in the northern city of Haifa three years ago on Sunday - the day of the Academy Awards ceremonies.
Paradise Now was nominated for
an Oscar for best foreign film
Seventeen people died in that attack by Hamas, which recently won Palestinian parliamentary elections.
"Paradise Now is a movie that attempts to explain away the actions behind mass murderers. This mere act, in effect, legitimises this type of mass murder and portrays the murderers themselves as victims!" the petition states.
A counter-petition in support of the film has drawn about 8300 online signatures. That petition says Paradise Now does not attempt to legitimise the bombings.
"It is a story about the suffering of Palestinians and how a life of desperation can lead to an act of desperation," according to the petition website.