The petition at change.org had almost 20,000 signatures late Thursday morning.
About 5,700 people were stopped on the course because of the explosions that killed three people and wounded hundreds more on Boylston Street on April 15. Ryan Polly of Vermont was approaching the 35K checkpoint when the bombs went off.
He started the petition, which asks for runners like him to be allowed to register in the 2014 race.
Boston Athletic Association officials say they can't make decisions about an expanded field before discussing it with the eight cities and towns along the course.