Gheybparvar was apparently referring to Trump's tweet in capital letters, in which he lashed out at Tehran and Iranian President Hassan Rouhani in particular.
He added, however, the war of words between the two presidents was to be expected, since official diplomatic relations between the two countries have been frozen for decades.
It is in response to Iranian president Rouhani telling him: 'American must understand well that peace with Iran is the mother of all peace and war with Iran is the mother of all wars'.
Iran is facing increased USA pressure and looming sanctions after Mr Trump's decision to pull out of the 2015 worldwide deal meant to prevent Tehran from developing nuclear weapons.
"You are not in a position to incite the Iranian nation against Iran's security and interests".
The recent anti-Iran tirades by the U.S. amount to "psychological warfare" and constitute interference in state matters, Tehran said, following Donald Trump's capitalized "consequences" tweet and Mike Pompeo's "mafia" remarks.
Iran can defend itself, Rouhani said.
"[Khamenei] said remarks by the president. that "if Iran's oil is not exported, no regional country's oil will be exported" were important remarks that reflect the policy and the approach of [Iran's] system", Khamenei's official website said on Saturday. The US president, a long-time critic of the historic 2015 nuclear deal with Iran, walked away from the agreement this May.
Pompeo also tweeted a succession of messages in Persian, trying to bring his message directly to any Iranians who are able to skirt their country's censors.
The timing of the heated remarks also raised the question of why Trump chose to issue his tweet late Sunday - after a week of negative attention for his meeting with Russian President Vladimir Putin last Monday, and the revelation that his attorney recorded him discussing hush money in 2016 that was paid to a woman who claimed she had an affair with Trump.
Trump has long-promised to take a hard line against Iran.
Trump's eruption on Twitter came after a week of heavy controversy about Russian meddling in the US 2016 election, following the Helsinki summit with Russian President Vladimir Putin.
The U.S.is set to reimpose economic sanctions on Iran in coming weeks, which will likely cause new problems for the country's struggling economy.
Iran's oil exports could fall by as much as two-thirds by the end of the year because of new United States sanctions, putting oil markets under huge strain amid supply outages elsewhere.