The paramilitary organisation said the projectile weighed 7kg (16lbs) and caused a "strong blast", killing Haniyeh and his bodyguard last Wednesday. The Hamas leader had been visiting the Iranian capital for the inauguration of President Massoud Pezeshkian.
The failures surrounding Haniyeh's death, especially on a day marked by intense security, have caused embarrassment for Iran and the IRGC.
Dozens of IRGC officers have been arrested or dismissed in the days since Haniyeh's death, the New York Times reported on Saturday.
The paper said the organisation's intelligence agency had taken over the investigation. Staff members at Haniyeh's guesthouse have been interrogated and their phones and other electronics have been seized, it added.
Meanwhile, the security details of Iranian politicians have been overhauled. Supreme Leader Ayatollah Ali Khamenei led prayers for Haniyeh on Thursday, but was whisked away soon after the ceremony by his security detail.
The IRGC's statement on Saturday came after Britain's Daily Telegraph said Haniyeh was killed by bombs planted in his room by agents of Israel's Mossad intelligence agency
Citing Iranian officials, the paper said two Mossad agents had entered the guesthouse and planted explosives in three rooms. The Iranians, who had viewed CCTV footage of the operatives, said the two subsequently left the country before detonating the bombs from outside Iran.
The New York Times also reported that Haniyeh was killed by explosives detonated in his room, saying they could have been planted up to two months earlier. The BBC has not been able to verify these claims.
But Hamas officials told the BBC earlier this week that Haniyeh had stayed at the same guesthouse before. He had made up to 15 visits to Iran since becoming the head of the political bureau in 2017.
The papers' reports - if true - would represent an even bigger failure for the IRGC, who have long controlled internal security in the country. Experts also said it would highlight the degree to which Mossad can operate with impunity in Iran.
Regardless of the manner of Haniyeh's death, both Iran and Hamas have vowed to retaliate.
The IRGC said on Saturday that Israel would receive "a severe punishment at the appropriate time, place and manner".
Hezbollah, the Iranian-backed militia and political group in Lebanon, has also vowed reprisals. One of their top commanders, Fuad Shukr, was killed in an Israeli strike last Tuesday.
After an Israeli operation killed IRGC Brig Gen Mohammad Reza Zahedi in Damascus earlier this year, Iran fired 170 drones, 30 cruise missiles and at least 110 ballistic missiles towards Israel.
Prime Minister Benjamin Netanyahu has warned Israelis that "challenging days lie ahead... We have heard threats from all sides. We are prepared for any scenario".
His ministers were sent home this weekend with satellite phones in case of an attack on the country's communication infrastructure.
Despite the government's warnings, the mood appeared relaxed on Tel Aviv's seafront, with bronzed bodies lazing under beach umbrellas.
But few are in any doubt that the Middle East stands perilously close to full-scale war.
Israel is on high alert and several international airlines have suspended flights to the country.
The US has also deployed additional warships and fighter jets to the Middle East to help defend Israel from possible attacks by Iran and its proxies, the Pentagon said.
UK Foreign Secretary David Lammy has warned that the risk that "the situation on the ground could deteriorate rapidly is rising".
Meanwhile, at least 10 have been killed in an Israeli airstrike on a school sheltering displaced in Gaza's Sheikh Radwan neighbourhood, the Hamas-run government media office has said.
It comes as Israel said an airstrike it conducted in the occupied West Bank killed a Hamas commander and four senior Palestinian Islamic Jihad fighters on Saturday.
The Israeli military said the air strike hit a vehicle as the men were on the way to carry out an attack.
Elsewhere, Israeli officials - including the directors of Mossad and the internal security agency Shin Bet - have arrived in Cairo for fresh ceasefire talks.
They will meet Egyptian intelligence chief, Abbas Kamel, and other senior military officials in a bid to rescue a potential truce. But US President Joe Biden admitted on Friday that Haniyeh's death had damaged the talks.
Haniyeh was heavily involved in negotiations and Mr Biden said his death “doesn’t help” efforts to end the ten-month old conflict.
The war began in October when Hamas carried out an unprecedented attack on Israel, killing 1,200 and taking 251 others back to Gaza as hostages.
The attack triggered a massive Israeli military response, which has killed at least 39,550 Palestinians in Gaza, according to the territory's Hamas-run health ministry.
The UK also told citizens to leave “while commercial flights are running.”
Iran says it will "punish" Israel for the assassination of Hamas leader Ismail Haniyeh.
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