He added: "Iranians have stood tall for a millennia while aggressors all gone".
The tensions have been rising in the area, as the USA has deployed additional warships and planes to the Gulf in recent days.
Zarif, who was educated in the United States, actually praised Trump for earlier remarks seen as pushing back against hawks in his administration who were encouraging conflict.
"I just don't want them to have nuclear weapons and they can't be threatening us", he said.
On Sunday a rocket was sacked into the Green Zone of the Iraqi capital Baghdad, which houses government offices and embassies including the United States mission. There were no claims of responsibility.
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 U.S. interests.
Mr Trump "hopes to achieve what Alexander [the Great], Genghis [Khan] & other aggressors failed to do". He ended his tweet with: "Try respect - it works!"
Meanwhile, Oman's minister of state for foreign affairs made a previously unannounced visit Monday to Tehran, seeing Zarif, the state-run IRNA news agency reported.
The drone strike on oil pumping stations, which Riyadh said did not disrupt output or exports, was claimed by the Houthis, who have been battling a Saudi-led military coalition in a war in Yemen since 2015.
The US president took to Twitter again on Monday, saying Washington has not tried to contact Iran for talks and that if the Islamic Republic wants to negotiate, it will have to take the first step.
Petraeus tempered his criticism, he said "the setting in which John gave that speech [advocating regime change] was to a bunch of Iranian dissidents essentially".
Two semi-official Iranian news agencies reported Monday that Iran now produces four times as much low-enriched uranium as before.
Administration officials plan to inform USA lawmakers on Tuesday about the threat they say that Iran poses to the country and US interests.
He said the acceleration of Iran's centrifuge enrichment machines remained within the bounds of the nuclear deal, and Tehran had no intention to exit the accord.
Meanwhile, the U.S. Navy's 5th Fleet on Sunday announced it would begin "enhanced security patrols" in global waters with members of the Gulf Cooperation Council, which includes Bahrain, Kuwait, Oman, Qatar, Saudi Arabia and the United Arab Emirates.
Prior to the agreement, Iran had the capacity to enrich uranium to up to 20 percent - well below the 90-plus percent required for a nuclear weapon, but still above the 3.6 percent limit required by the deal. Iran denied their involvement in the attack.
The USS Abraham Lincoln is now sailing in the Arabian Sea. Following Sunday evening's events, prominent Iraqi Shiite cleric Muqtada al-Sadr and several other Iraqi politicians warned against dragging Baghdad into a conflict between Iran and the United States.
Saudi Arabia, the United Arab Emirates, Bahrain and Egypt are among the countries that cut ties with Qatar in June 2017 over accusations it supports terrorism and seeks closer ties with Tehran.