Burn Valley councillor Jonathan Brash has asked council chiefs to look at potential measures in the Park Road area following the incidents and calls by residents.
A female school crossing patrol warden suffered a broken leg and facial injury after a collision involving a car on Park Road near Eldon Grove on Friday, May 28.
An ambulance went to her aid and police are looking into the circumstances.
Then on bank holiday Monday a girl was taken to hospital by ambulance after a report she was in a collision with a vehicle in Hutton Avenue nearby.
Hartlepool Borough Council said it is investigating the Park Road incident and Hutton Avenue has been added to its list of areas for potential measures.
Cllr Brash said: “First and foremost my thoughts are with the victims and I hope they are both making good recoveries.
“Road safety has to be one of our top priorities and residents have been in touch following these accidents to say that incidents like this are all too common.
"I have said in both cases the council needs to have an urgent review of road safety in the area to see what measures can be put in place.”
He appealed to motorists across town to take extra precautions when driving.
A council spokesman said: “Road safety is a top priority, so both incidents are matters of concern.
“As with all accidents involving school crossing patrollers, an investigation is underway to assess whether any measures are needed to prevent similar incidents occurring in the future.
“Electronic 20mph signs have recently been installed either side of the crossing and they will shortly be operational.
"Hopefully, the signs will improve the safety of the crossing, but we will continue to monitor the situation closely.
“We have added Hutton Avenue to the council’s list of Local Safety Schemes and, along with the many other requests we receive for road safety improvements across the borough, it will be assessed in line with agreed criteria to determine our priorities within the resources we have available to us.”