The two people killed were "members of the Basij forces", a paramilitary force affiliated with the Revolutionary Guards, the ideological arm of the Iranian military, Tasnim said.
Tasnim did not specify the date of the incident or the identity of the attackers, but said that "the perpetrator or perpetrators of this act will be punished".
According to the agency, the two men were killed while "patrolling in the city of Mashhad, about fifteen kilometres (nine miles) from the shrine" of Imam Reza, the holiest site for Shia Muslims in Iran, where Ali Khamenei was buried early Friday.
"A pedestrian was also wounded by the attackers and taken to hospital," the Iranian agency added.
The late supreme leader was killed in US-Israeli strikes on February 28, at the very beginning of the war in the Middle East.
Hostilities resumed this week between Iran and the United States, exchanging their most intense strikes since they signed a memorandum of understanding last month that formalised a ceasefire agreed in April.
