Sisters Lily and Shelley Wu, aged seven and six, were injured while crossing a road in Handsworth, Birmingham.
Wilkes Green Infant School said: "Staff and pupils are deeply saddened by the loss and by the impact on the family."
The girls' mother, 39, is in a critical condition and her son, 13, and 12-year-old daughter were also badly injured.
The school, which is understood to have held a special assembly to remember the girls, added: "We have arranged support for staff and pupils and will be keeping in contact with the father of the girls."
A 34-year-old local man who was arrested at the scene on suspicion of dangerous driving has been released on bail.
Police have appealed for witnesses to the incident which happened near the junction of Grove Lane and Antrobus Road about midday on Sunday.
Residents of Grove Lane have called for a meeting with Birmingham City Council to improve safety on the road which has seen a number of accidents recently, including another fatal crash.
City councillor Waseem Zaffa said people living nearby had already spoken the police and council's transport department but were waiting for the results of the police investigation into the crash.
"We will be - as soon as possible after these investigations and initial findings - looking to rectify the issues with this particular junction and the wider Grove Lane area," he said.
Pupils at a Birmingham primary school are being offered support following the death of two children who were struck by a car on Sunday.