In an exclusive interview with CNN on Tuesday, Zarif warned that the US was "playing a very, very dangerous game" by boosting its military presence in the region.
The Minister's remark comes after Trump in a series of tweets on Sunday asked Iran "never to threaten" the US and warned Tehran that if it wants a fight, it would be "the official end" of the Islamic nation.
"Iran never negotiates with coercion. You cannot threaten any Iranian and expect them to engage. The way to do it is through respect, not through threats," the Minister said.
Zarif said there "will be painful consequences if there is an escalation", but added that Iran was "not interested in escalation".
Instead, he called for an immediate end to the "economic warfare" waged by the US on Iran, saying that sanctions were "depriving citizens of their means of livelihood".
"All we want to do is sell our oil," Zarif said, adding that the US was "just a bully preventing people from buying our oil".
He said the US sanctions, which have hit the Iranian economy hard, "amounts to terrorism" on the country's citizens.
Zarif also accused Washington of walking out first on the Joint Comprehensive Plan of Action (JCPOA), the 2015 deal designed to limit Iran's nuclear capabilities in return for the lifting of sanctions.
"We acted in good faith," Zarif told CNN of the deal, which was signed by the US, Iran, Britain, China, France, Germany and Russia. "We are not willing to talk to people who have broken their promises."
Iran has announced it would be partially withdrawing from the deal on the one-year anniversary of the US's departure from the accord. It gave the remaining signatories until July 7 to ease restrictions on Iran's badly hit banking and oil sectors, or face unspecified retaliation.
The Minister also criticized the US for sending the USS Abraham Lincoln carrier strike group and a bomber task force to the Persian Gulf.
"Having all these military assets in a small area is in of itself prone to accidents," Zarif said. "Extreme prudence is required and the US is playing a very, very dangerous game."
( With inputs from IANS )