The Wednesday attacks involved gunmen storming Iran's Parliament (Majlis) and the Mausoleum of the late founder of the Islamic Republic, Imam Khomeini, in two coordinated attacks.
Iran has indirectly suggested that Saudi Arabia, its major regional rival and a US ally, played a role in the attack.
During the funeral, Parliament Speaker Ali Larijani called the USA the "international" version of the Islamic State group and said Washington had exchanged democracy for money, a reference to a recent huge arms deal between the US and Saudi Arabia.
The pragmatist president championed a nuclear deal with the United States and five other powers in 2015 that led to the lifting of most sanctions against Iran, in return for curbs on its nuclear programme.
After prayers at Tehran University, a long procession left central Tehran for Behesht-e-Zahra cemetery near the Khomeini mausoleum, 20 kilometres (12 miles) away.
IS claimed responsibility and threatened more attacks against Iran's majority Shi'ite population, seen by the hardline Sunni militants as heretics.
The intelligence ministry on June 8 revealed the identities of the five attackers and said they had fought for the IS in Iraq and Syria.
Security was tightened around the country to prevent other possible plots.
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Shiites make up roughly 90 percent of Iran s population, but the country also has a sizeable Sunni minority, particularly around its restive borders with Iraq and Pakistan.
The ISIS Takfiri terrorist group claimed responsibility for the near-simultaneous assaults. "We obey Allah and His Messenger, and we are fighting for the sake of this religion, not for the sake of Iran or the Arabian Peninsula".
That drew fire from Iran s foreign minister, Mohammad Javad Zarif, who tweeted: "Repugnant WH (White House) statement.as Iranians counter terror backed by U.S. clients".
Saudi Arabia has denied involvement, Reuters reports.
Iran's Revolutionary Guards have suggested that the attack was linked to Saudi Arabia. During the operation to arrest the terrorists, large amounts of weapons, bomb-making materials, explosive belts, communication equipment, and forged documents had also found, it added.
Iran's Supreme Leader is saying that the Islamic State-claimed dual attacks that killed 17 people in Tehran will add to the hatred that Iranians harbor toward the USA and Saudi Arabia.
A nationwide hunt has uncovered explosive vests and other equipment, as well as an abandoned auto containing at least 22 pistols, in Kermanshah province.
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