Raisi accused "imperialist powers" of being behind the assassination, which was carried out on Sunday in a neighbourhood in the southeast of the Iranian capital Tehran.
The term is used in Iran as a reference to Israel and the United States.
The victim, Hassan Sayad Khodayari, was reportedly a member of the Quds Force, one of five branches of the Revolutionary Guards who fight against the Islamic State group in Syria and Iraq.
His attackers fired five shots before fleeing on a motorcycle, according to the IRNA news agency.
They have not been detained and details of the attack remain unclear.
Khodayari's precise role in the IRGC is also not known.
He is reported to have been a "defender of the sanctuary," a term used to describe members of elite units protecting Shi'ite shrines outside Iran.
He was shot in his own small car and was without bodyguards, according to reports.
Senior IRGC personnel usually travel under escort and in armoured vehicles.
The IRGC reported on Sunday that they had arrested suspected members of a network of the Israeli secret service Mossad.
According to the IRGC website, "rioters" allegedly working for Mossad in Iran had been arrested on suspicion of kidnapping and theft, among other things.
Israel has been considered Iran's arch-enemy since the 1979 Islamic Revolution.
There are repeated reports of arrests, detentions and executions of suspected agents accused of cooperating with Mossad or the US foreign intelligence service CIA.
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