TORONTO -- The family of an 11-year-old Toronto girl has reportedly apologized for the "pain and anger" they caused, after the girl's claim that a man cut her hijab turned out not to be true.

"This has been a very painful experience for our family," said the statement, first reported by the Toronto Star.

"We want to thank everyone who has shown us support at this difficult time. Again, we are deeply sorry for this and want to express our sincere apologies to every Canadian."

Toronto police began investigating the alleged incident as a hate crime last Friday, after the girl said she was attacked twice on the way to school by a man who cut her hijab with scissors.

The alleged incident made international headlines and drew swift public condemnation from the prime minister, Ontario's premier and Toronto's mayor.

On Monday, police announced that their investigation was complete and the alleged incident did not happen.

They said no charges would be laid.

Spokesman Mark Pugash said in an interview that police weren't prepared to discuss how the situation escalated.

He stressed that it's "very unusual" for someone to make such false allegations, and he hopes it will not discourage others from coming forward.

Canadian Muslim organizations expressed similar concerns, saying they feared others who experience hate crimes may be reluctant to report them out of worry that they will not be believed.

In their statement Wednesday, the girl's family said when they heard her story, they "assumed it to be true, just like everyone else."

They added, "We only went public because we were horrified that there was such a perpetrator who may try to harm someone else."