The boy’s grandmother said the attackers taunted him with racial slurs on 28 August in the mostly white town of Claremont, before pushing him off a picnic table with a rope around his neck.
He was treated in hospital for injuries to his neck and has been released.
Claremont Police Chief Mark Chase said his department was investigating a “serious incident” involving juveniles in which a child was hurt, but did not provide further details.
Rebecca MacKenzie, from Claremont, said she organised the rally on Tuesday to draw attention to racial intolerance and xenophobia.
“Claremonters are good people and, even as good people, we need to face the facts of racial injustice and begin a deep dialogue of how to deal with it in our community,” she said.
Republican Governor Chris Sununu has asked the state attorney general’s office to help with the investigation.
“Hatred and bigotry will not be tolerated in NH,” he tweeted.
Relatives posted images of rope burns on the boy’s neck to social media and details of the alleged attack.
Democratic congresswoman Annie Kuster said she was “outraged and sickened by the chilling images on social media and in the news”.
Biracial families from towns around Claremont said they had friends who had been racially abused or assaulted because they are not white.
Karen Liot Hill, a city councillor and former mayor of Lebanon, said: “As a mother of a biracial child, this incident sent a chill through my entire body… it broke my heart.”