Reportedly, two guards, 10 staffers and five others were killed during the attacks that simultaneously targeted the country's parliament and shrine of late founder of the Islamic Republic Ayatollah Ruhollah Khomeini.
After prayers, a procession was to leave Tehran University for the Behesht-e-Zahra cemetery, near the Khomeini mausoleum 13 kilometres south of the Iranian capital.
"Allah permitting, this brigade will be the first of jihad in Iran, and we ask our brothers the Muslims to follow us, as the fire that was ignited will not be put out, Allah permitting", one of the masked fighters said, according to SITE.
"We grieve and pray for the innocent victims of the terrorist attacks in Iran, and for the Iranian people, who are going through such challenging times", the statement said.
Iran's Intelligence Ministry said Thursday that five of the men involved in the attacks were Iranians who had joined IS.
Egypt has condemned Islamic State-claimed attacks on Iran's parliament and a shrine to its revolutionary leader in the "strongest terms".
Riyadh and Washington both condemned the attacks, which came soon after Saudi Arabia and other Sunni-ruled countries cut ties with Qatar over its alleged support for Islamist militants and closer ties with Iran. The Isis terror group claimed responsibility for what it is thought to be the first attack linked to the militants in Iran.
Following deadly attacks on Tehran on June 7, Iran has initiated a response, targeting those responsible for the attacks.
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But Intelligence Minister Mahmoud Alavi has said "we still can not judge that Saudi Arabia has had a role in this terrorist incident".
Also, the attack comes against a backdrop of regional tension, with Arab Gulf countries pushing for a more forceful isolation of Iran.
The Saudi's have denied involvement in the attack.
Seventeen people were killed last week in a terror attack claimed by IS in Tehran.
The ministry also published pictures of their corpses.
When Daesh (ISIS) called on members of Iran's Sunni minority in March to wage a religious war on their Shiite rulers, few people took the threat seriously.
"Death to America", "Death to the Saud" ruling family, and "We are not afraid", shouted the crowd behind a lorry bearing the coffins of 15 of the 17 people killed.
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