"The five known terrorists. after joining the Daesh (IS) terrorist group, left the country and participated in crimes carried out by this terrorist group in Mosul and Raqa", the intelligence ministry said in a statement.
Iranian authorities have said assailants were Iranian nationals, adding they have arrested six suspects, including one woman, since the attack Wednesday in Tehran.
The ministry did not identify the men's home towns or say how they were able to evade authorities.
Iran blamed the Wednesday attacks on Saudi Arabia, casting them in the context of a broader regional conflict that encompasses the war inside Syria.
Commuters in the Iranian capital noticed police on street corners and motorcycles, more than usual as dawn broke. That came after Mohammad Hossein Zolfaghari, a deputy Interior Minister, told state TV that "law enforcement activities may".
"We are focused on intelligence" gathering, he said.
State television reported the increase Thursday, citing Ahmad Shojaei, the head of the country's forensic center.
Police patrol outside Iran's parliament building after an assault by several attackers that was claimed by the Islamic State group, in Tehran, Iran, Wednesday, June 7, 2017.
IS has regularly threatened Iran, which is backing militias battling IS fighters in both Iraq and Syria.
Qatar vows no surrender in Gulf crisis as US, Kuwait seek solution
He said Qatar, as an independent nation, also had the right to support groups like the Muslim Brotherhood, despite the fact that its neighbors outlawed the Sunni Islamist organization.
President Donald Trump in a statement suggested that Iran bears some culpability for attacks in its capital.
The White House released a statement from Mr Trump condemning the terrorist attacks in Tehran and offering condolences, but also implying that Iran is itself a sponsor of terrorism.
Trump had said he prayed for the victims of Wednesday's attacks that were claimed by Islamic State, but added that "states that sponsor terrorism risk falling victim to the evil they promote".
The comments sparked anger from Iranians on social media, who recalled the vigils in Tehran that followed the September 11 attacks.
Iranian Foreign Minister Mohammad Javad Zarif took to Twitter to denounce Trump's reaction to the attacks and moves by USA lawmakers to slap new sanctions on Iran. "Iranian people reject such U.S. claims of friendship", said in a tweet.
Sunni Gulf Arab states are in the midst of a major diplomatic crisis after Saudi Arabia and its allies cut ties with Qatar on Monday over claims it supports extremism and has fewer tensions with Iran. "They look for a way to destabilize our country".
Supreme Leader Ayatollah Ali Khamenei sought to play down the Tehran attacks, calling them mere "firecrackers" that would have no effect on "the will of the people". He told a group of students that if "Iran had not resisted", it would have faced even more troubles.
IS has threatened to step up recruitment within Iran, releasing its first Persian-language video in March in which it threatened to "conquer Iran and restore it to the Sunni Muslim nation as it was before".
The attackers were armed with rifles and pistols and at least two blew themselves up with suicide vests, Iranian media reported.