The four family members killed were: Salman Afzaal, 46; his wife, Madiha Salman, 44; their 15-year-old daughter, Yumnah Afzaal; and Afzaal's 74-year-old mother, whose name has not yet been released. 

Their 9-year-old son, Fayez Afzaal, is in hospital with serious but non-life-threatening injuries. 

A 20-year-old suspect is in police custody and has been charged with murder. In a statement on Tuesday, the family contradicted the initial police appraisal that he was not a member of any hate group and had no accomplices. 

"The young man who committed this act of terror was influenced by a group that he associated with, and the rest of the community must take a strong stand against this...," the family said in a statement. 

"We need to stand against hate and Islamophobia and raise awareness in our communities and across all the political spectrum," it said. 

Police, citing witnesses, said that 20-year-old Nathaniel Veltman, jumped the curb in his vehicle and struck five members of the family. Veltman, who had no previous criminal record, has been charged with four counts of first-degree murder and one count of attempted murder. He is due back in court on Thursday after being remanded to custody on Monday. 

The family called the attack brutal and horrific, and said the children had both been top students and their parents excelled in their fields. 

"Everyone who knew Salman and the rest of the ... family know the model family they were as Muslims, Canadians and Pakistanis. They were always there giving and participating in spreading goodness," it said. 

The family has declined to comment further and asked to grieve in private. 

The attack was the worst against Canadian Muslims since a man gunned down six members of a Quebec City mosque in 2017.