In separate phone calls, Raeisi, who is also the chairman of the Supreme National Security Council (SNSC), urged the two officials to fully utilize available resources for the proper care of the injured.
The Iranian president ordered Vahidi to diligently and swiftly investigate the security dimensions of the incident and report the result.
He extended his condolences to the bereaved families of the victims.
At least one person was killed and eight others injured in an armed terrorist attack at the Shah Cheragh shrine in Iran's southern city of Shiraz.
State media reported two terrorists were involved in the shooting on Sunday. One of the assailants was arrested. The other is said to be at large.
Three of those injured in the attack were in critical condition.
The ISIL terrorist group claimed responsibility for the deadly assault.
MNA/PressTV