But US defence secretary Jim Mattis called Iran's claims of US involvement "ludicrous", and told reporters he was not concerned by the threats.
"We promise to show an annihilating and destructive response which makes them (the culprits) regret their deeds and no one will be able to kill our children in this territory, and this will not be the end of the story and we warn everyone that we will take revenge", said Brig. "And I am hopeful that cooler, wiser heads will prevail".
An Iranian media outlet close to the hard-line Revolutionary Guard published a video Tuesday threatening missile attacks on the capitals of Saudi Arabia and the United Arab Emirates, further raising tensions after a weekend militant attack on an Iranian military parade.
The coffins, wrapped in the flag of the Islamic Republic, were carried by the mourners.
The victims of the assault included civilians and members of the elite Islamic Revolutionary Guards Corps (IRGC).
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A statement reported by the semi-official Tasnim news agency also said "weapons, exclusive material and communication equipment were seized".
Giuliani has made similar comments before on Iran and the State Department has said he does not speak for the administration.
Iranian concerns about US interference are linked more to John Bolton, now US President Donald Trump's National Security Adviser who spoke in support of MEK as an alternative to the Iranian government at the group's annual conference in 2017.
Khamenei said those behind the "terrorist attack" were funded by Saudi Arabia and the United Arab Emirates.
Guards Brigadier General Hossein Salami, in a speech broadcast on state TV, said: "You have seen our revenge before". Indeed, his personal lawyer, Rudolph Giuliani, boasted on Saturday that USA sanctions are hurting Iran: "I don't know when we're going to overthrow them".
The attack targeted a military parade commemorating the anniversary of the 1980-1988 Iran- Iraq war.
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Saturday's assault, one of the worst ever against the most powerful force of Iran, struck a blow at its security establishment at a time when the United States and its Gulf allies are working to isolate Tehran and are hoping for a regime change in the country.
This year's parades had special significance as tensions with the United States have peaked since the USA withdrew from the 2015 nuclear deal in May and began to re-impose unilateral economic sanctions on Tehran.
Iran's Intelligence Ministry on Tuesday identified the attackers as Hassan Darvishi, Javad Sari, Ahmad Mansouri, Foad Mansouri and Ayad Mansouri. "The small (Arab) puppet countries in the region are backed by America, and the U.S.is provoking them and giving them the necessary capabilities".
It is, however, highly unlikely the Guards will strike any of its foes directly and risk setting off a regional conflict.
Karim Dahimi, a human rights activist in London, told Reuters local sources had said more than 300 people had been arrested in the cities of Ahvaz, Khorramshahr and Abadan in recent days, mostly from the Sunni Muslim community.
At least two of the men have appeared in a video distributed by the Islamic State group in its own claim of responsibility for the Ahvaz attack.
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