He also said Iran had obtained intelligence showing that Saudi Arabia was "actively" propping up terrorist groups along Iranian eastern and western borders. The attacks were later claimed by Daesh (ISIS).
Iran's Supreme leader Ayatollah Ali Khamenei has accused the US of destabilizing the Middle East by providing support to extremist groups active in the region.
A terrorist attack claimed by ISIS on Iran last week killed at least 17 people.
On September 11, 2001, 19 terrorists - 15 of them Saudi nationals - engaged in a multi-pronged attack on USA soil, including hijacking passenger planes and crashing them into what were then the twin towers of the World Trade Center in New York City.
Ayatollah Khamenei also broached the subject of the US's increased saber-rattling and further sanctions following Iran's recent presidential election.
Speaking about Iran's nuclear deal with the P5+1 group of countries in 2015, Ayatollah Khamenei called on Iranian officials to carefully monitor the other parties to see if they are honoring their side of the agreement.
Iran and Saudi Arabia has been accusing each other of subverting regional security and support opposite sides in conflicts including those in Syria, Yemen and Iraq. In the view of many Iranians, wherever they stand on the country's reformist-conservative axis, any lack of political or social freedom in the Islamic Republic is a price worth paying for a secure state, and they have dreaded the day when - if - that security would come to an end.
On Tuesday, Iran's Foreign Minister Mohammad Javad Zarif referred to those remarks by the Saudi officials and called them a "direct threat and very risky provocation" by Riyadh.
Iran's Revolutionary Guard quickly, but with deliberate vagueness, incriminated Saudi Arabia and the United States.
Zarif arrived in Norway on Monday to participate in the 15th Annual International Retreat of Mediators and Peace Process Actors in Oslo Forum. The fingers of blame were pointed at Saudi Arabia and the United States, who were accused of being behind the attacks.