Five attackers stormed Iran's parliament and a shrine to revolutionary leader Ayatollah Ruhollah Khomeini on Wednesday, setting off clashes with security forces and killing 17 people.
Alavi also added that the safe house used by the five terrorists who carried out the attacks in Tehran was discovered by security forces and the brother of one the terrorists, who according to the minister was even more unsafe, was caught by the intelligence forces.
Iran has said five Iranians, who had joined IS and travelled to its Iraq and Syria bastions, carried out the attack.
The Tehran Security Council had convened an emergency meeting after two terror attacks occurred on the Iranian Parliament and Imam Khomeini Mausoleum respectively on Wednesday.
At least 12 people were killed when six attackers mounted simultaneous gun and suicide bomb attacks on Iran's Parliament building and the tomb of the republic's revolutionary founder, in one of the most audacious assaults to hit Tehran in decades.
Iranian authorities have also arrested seven people it suspects of helping militants involved in attacks, a judiciary official said on Saturday.
Ali Asghar Gorjizadeh, the commander of IRGC's Ansar-ol-Mahdi Corps, which is responsible for protection of senior Iranian officials, said in a televised interview on Saturday that from the very first moments after the twin terrorist attacks, members of the Ansar-ol-Mahdi Corps took measures to encounter the terrorists.
He noted that the extremist had fled the country following the ensuing security operations after the attack, but was killed with the cooperation of friendly foreign intelligence services. Members of Iranian forces are seen during a terrorist attack on the Parliament in central Tehran, Iran, on June 7, 2017.
Forty-three suspects were detained on Saturday and operations to identify and crush more "terrorists cells" were under way, Mr Alavi said.
Eight others have been arrested in the Alborz Province in connection with the attacks, according to reports by state news agencies.
Tehran police said the auto the attackers used on Wednesday was discovered on Saturday in the city centre.