Trump responded in all caps, warning Rouhani against "ever threatening the USA again", stressing potential dire consequences "the likes of which few throughout history have ever suffered before".
Iran is facing increased United States 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.
"Mr Trump, don't play with the lion's tail, this would only lead to regret", Rouhani told a group of diplomats, according to Reuters, citing the semi-official ISNA news agency. The deal had been a core component of former President Barack Obama's legacy, offering Tehran sanctions relief in exchange for a halt to Iran's nuclear ambitions.
Trump's tweet late on July 22, mainly in capital letters, came hours after Rohani had warned Trump against pursuing hostile policies against Tehran. The U.S. president supported the protests, saying "the people of Iran are finally acting against the brutal and corrupt Iranian regime".
Blocking world leaders on Twitter won't silence them, but it would certainly hamper necessary discussion around their words and actions, the company said.
Prime Minister Benjamin Netanyahu commended Trump's "tough stand" against Iran. "That would be a determination that the President would make.But the ultimate goal and the focus of the President is making sure we keep nuclear weapons out of their hands and that we focus on the protection of America", she said.
Trump directly addressed the Iranian leader with his threat.
Trump's national security adviser John Bolton has in the past advocated bombing and invading Iran to enact regime change.
Iranian officials accused the White House of waging "psychological warfare" and vowed to resist any US efforts to destabilize their government.
Mr Pompeo said: "The proud Iranian people are not staying silent about their government's many abuses".
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