Ayatollah Ali Khamenei blamed USA for the creation of ISIS and also said that it's fight against Islamic State is a lie.
Dozens of suspects have been arrested since the attacks on Wednesday killed 17 people in the first assault in Iran to be claimed by the Islamic State jihadist group.
Riyadh has denied involvement in the suicide bombings and gun attacks on Iran's parliament and the mausoleum of the Islamic Republic's founder, Ayatollah Ruhollah Khomeini. Who created Islamic State?
"In [the Iranian month of] Ordibehesht [started April 21] we have uncovered such teams on a daily basis".
Several suspected militants, including the alleged mastermind of twin attacks in Tehran last week, were tracked down, detained or killed by Iranian authorities, a security official and a minister confirmed.
It comes as relations between Tehran and Washington have grown increasingly strained, most recently overshadowed by a string of allegations made by a number of high-ranking Iranian officials claiming the USA had forged an alliance with Islamic State (IS, formerly ISIS/ISIL).
Iranian President Hassan Rouhani, who favours opening up to the world, has condemned the attacks, without pointing a finger at any country.
But the deal has not led to normalisation of ties between the two countries that Rouhani hoped for.
The statement said: "And may the people of Iran come out of this tragedy more united and triumphant".
Weighing on the chances of Iran-US relations improving, Khamenei said there was hardly any room for rapprochement, arguing that Washington is against the very idea of "an independent Iran", Reuters reported.
Ayatollah Amoli Larijani stressed that Iran's conduct in the fight against terrorism in known to everyone, but the hegemonic powers and their allies in the region have made up a big lie about forming a coalition against Daesh while they provide all-out support for the terrorist group. "Most of our problems with them can not be resolved", the semi-official Fars news agency quoted him as saying.
"America is a terrorist country and backs terrorism. therefore, we can not normalise ties with such country", he said.