"Iranians have stood tall for millennia while aggressors all gone. Economic terrorism and genocidal taunts won't 'end Iran'," Zarif wrote on Twitter.
"Never threaten an Iranian. Try respect -- it works!" he added.
The riposte by Iran's top diplomat follows an ominous warning by Trump, who on Sunday suggested the Islamic republic would be destroyed if it attacked US interests.
"If Iran wants to fight, that will be the official end of Iran. Never threaten the United States again," Trump tweeted.
Relations between Washington and Tehran plummeted a year ago when Trump pulled out of a landmark 2015 nuclear deal with Iran and imposed tough sanctions.
Iranian officials have repeatedly slammed the unilateral US sanctions as "economic terrorism," saying that they have impeded the flow of essential goods.
Tensions have risen further this month with Washington announcing more economic measures against Tehran, before deploying a carrier group and B-52 bombers to the Gulf over unspecified alleged Iranian "threats".
The Trump administration last week ordered non-essential diplomatic staff out of Iraq, citing the danger posted by Iranian-backed Iraqi armed groups.
On Sunday a rocket was fired into the Green Zone of the Iraqi capital Baghdad, which houses government offices and embassies including the US mission. It was not immediately clear who was behind the attack.
While the US claim of Iranian "threats" has been met with widespread scepticism outside the United States, the mounting tensions have sparked growing international concern.
"I would say to the Iranians, do not underestimate the resolve on the US side in the situation," British foreign minister Jeremy Hunt told reporters on Monday in Geneva.
"They don't want a war with Iran, but if American interests are attacked they will retaliate," he added.
Hunt said that Britain wanted "the situation to de-escalate" and urged Iran "to pull back from the destabilising activities it does throughout the region."
- 'Goaded' into war -
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US media reports say Trump's hawkish national security advisor John Bolton is pushing for war with Iran, but others in the administration are resisting.
Zarif's tweet said Trump is being "goaded by B Team," a term he coined to refer to Bolton as well as Israel's prime minister and the crown princes of Saudi Arabia and United Arab Emirates who are all pushing a hard line on Tehran.
Before Trump's Twitter threat Zarif had downplayed the prospect of a new war in the region, saying Tehran opposed it and nobody was under the "illusion" the Islamic republic could be confronted.
Iran is exercising "maximum restraint" in the face of an "unacceptable" escalation by the United States, Zarif said on Thursday.
Tehran has threatened to gradually withdraw from the 2015 nuclear deal if partners still in the agreement -- Britain, China, France, Germany and Russia -- do not help it to circumvent US sanctions.
Saudi Arabia on Saturday called for emergency regional talks to discuss the mounting Gulf tensions.
It came days after mysterious sabotage attacks on several tankers in highly sensitive Gulf waters and drone strikes on a Saudi crude pipeline by Yemen rebels who Riyadh claimed were acting on Iranian orders.
Saudi Arabia's minister of state for foreign affairs, Adel al-Jubeir, said Sunday his country does not want to go to war with Iran but would defend itself.
Saudi Arabia "does not want a war, is not looking for it and will do everything to prevent it," he said.
"But at the same time, if the other side chooses war, the kingdom will respond with strength and determination to defend itself and its interests."
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