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.
Raeisi stressed that all those who have been somehow involved in this terrorist attack must be identified and brought to justice.
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 Daesh terrorist group claimed responsibility for the deadly assault.
Iran FM warns of painful end for terrorists
In a post on his X social media account, Iranian Foreign Minister Hossein Amir-Abdollahian strongly condemned the terrorist attack in Shiraz and warned of a “painful end” for the perpetrators and supporters of the heinous crime.
“The terrorist operation in the holy shrine of Hazrat Shah Cheragh is strongly condemned,” Amir-Abdollahian said.
“A painful end awaits the perpetrators and supporters of this crime. While condoling the martyrdom of one of my compatriots, I ask Almighty God for the health and recovery of those injured in this tragic incident,” he tweeted.
The Shah Cheragh shrine in Shiraz was the scene of a similar attack by armed terrorists last year.
On October 26, 2022, an armed terrorist barged into the shrine, killing 15 pilgrims, including women and children, and injuring dozens more before he was shot and injured by security forces.
The terrorist later died of his wounds in hospital.
Several suspects were immediately arrested, and, some two weeks later, the Intelligence Ministry announced the arrest of 26 Takfiri terrorists for their involvement in the attack.