Saturday's attack, in which militants disguised as soldiers opened fire on an annual Iranian military parade in Ahvaz, was the deadliest attack in the country for nearly 10 years. Iranian leaders blame the USA and Israel for the carnage, and vowed revenge.
The deputy head of the Revolutionary Guards meanwhile warned the United States and Israel to expect a "devastating" response, accusing them of involvement.
"Iran will respond swiftly and decisively in defense of Iranian lives", Zarif wrote on Twitter.
"We've been very clear that they shouldn't take us on like that", he said.
In response, Mattis said, "It would be good if they knew what they were talking about", adding that he hoped "cooler and wiser heads would prevail".
Four assailants fired on a viewing stand where Iranian officials had gathered to watch the annual event marking the start of the Islamic Republic's 1980-88 war with Iraq.
The victims of the assault included civilians and members of the elite Islamic Revolutionary Guards Corps (IRGC). "Lie down! Lie down!" one man screamed as a woman fled with her baby.
Thousands of people packed the streets of the southwestern Iranian city of Ahvaz to mourn the victims.More news: Cosby back in court for sentencing
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The secretary of Iran's National Security Council said Tehran needed to talk to its neighbours to avoid tensions.
Who was behind the attack?
Iran's Ground Force General Nozar Nemati was quoted as saying by Mizan news agency that "the agents behind this attack are identified and will be published at the appropriate time".
Haley said Washington was trying to counter Iranian malign activities in the region as Tehran continued to test ballistic missiles, support terrorism and sell arms.
He also said USA sanctions against Iran were illegal and President Donald Trump was using them as a tool for "personal revenge".
Two groups have claimed responsibility for the attack: the ethnic Arab antigovernment Ahvaz National Resistance and the extremist group Islamic State (IS).
The footage, released by the Amaaq news agency, shows three men in a vehicle, apparently on their way to carry out the attack. However, none of them stated that they were members of IS or pledged allegiance to the group's leader, Abu-Bakr al-Baghdadi - something that is common in such pre-attack videos. "He unjustifiably quit the deal, threatened the Iranian people for no reason and intervened in our internal affairs". Gen. Esmayeel Kossari, said the reactions in Saudi Arabia and the United Arab Emirates - along with "documents" that he said had been found in Iraq and Syria - were proof that "the Americans gave orders to Riyadh and supported this attack".