Police officers arrested a 43-year-old man after two 11-year-old girls reported being attacked outside a Vancouver elementary school, but now the force believes no such attack happened.

The Vancouver Police Department says it believes "the story provided by the girls alleging that they had been assaulted was false and that no assault took place."

The two girls, who were playing on a field adjacent to Strathcona Elementary School at around 4:30 p.m. PT Sunday, allegedly got into an argument with the man over the ownership of one of their backpacks.

The girls then ran home and reported the incident to their parents, who in turn called police.

On Tuesday, tips from members of the public identified the man the girls described, and a 43-year-old Vancouver man was taken into custody as the suspect.

Police now say that a witness to the incident on the field came forward, and gave a different story than the girls'. Police officers spoke to the girls again, and determined the alleged assaults didn't happen.

"Vancouver Police Youth Services is now working with the girls and their families to assist in any way needed, and to help ensure the girls understand the gravity of their actions," the department said in a written statement.

As the girls are under 12 years of age, the force said it is not pursuing charges of public mischief against them.