Iranian Foreign Ministry spokesman Bahram Qasemi also responded to Trump's offer by noting that it was in contradiction his actions of imposing sanctions and pressuring other countries into avoiding business with Tehran. A round of new US sanctions are set to be imposed on Iran early next week.
But other changes in US policy will be trickier.
"If Trump is really into any talks with Iran, he should first amend the broken trust and then speak about negotiations", Masoud Goudarzi, a member of the Iranian parliament's national security and foreign policy commission, said Tuesday, according to ISNA.
Mr Rouhani's interior minister, Abdolreza Rahmani Fazli, said that there would not be a positive response to any invitation.
Mr. Trump's brusque tone hasn't endeared him to Iranian officials, either. "If the current capabilities of the Revolutionary Guards ... reaches the ears of the adventure-seeking president of America, he will never make this kind of mistake and will reach the understanding that an oil threat can be easily answered", Jafari said.
It's possible that Trump doesn't really want to meet with Iran's leaders.
Relations of the two nations have been at odds as the Trump administration pulled the United States out of the historic 2015 Iran nuclear deal in May.
Under the 2015 deal, the fruit of Rouhani's efforts to ease Iran's worldwide isolation to help revive its economy, Iran curbed its nuclear program and won relief from United Nations and Western sanctions in return.
Some will be reimposed in August and target autos, gold and other key metals, while others will snap back in November and target the energy sector and transactions with Iran's central bank. President Barack Obama broke a three-decade freeze with a phone call to Rouhani in 2013.
Mr Rouhani's chief of staff claimed earlier this month in Iran's state-owned newspaper that Mr Rouhani had rejected eight requests from Mr Trump for one-on-one talks previous year.
Speaking at a press conference alongside Italy's Prime Minister Giuseppe Conte, the President said "I believe in meeting". "I don't know that they're ready yet; they're having a hard time right now".
In May Mr Pompeo laid out 12 conditions for any "new deal" with Iran, including the withdrawal of its forces from Syria and an end to its support for rebels in Yemen. It was a ridiculous deal. I'm ready to meet any time they want to.
The U.S. leader cited his experience meeting with North Korean leader Kim Jong Un in Singapore last month as a sign of his willingness to help address concerns of war and peace.
Heshmatollah Falahatpisheh, who heads the parliamentary committee on national security and foreign policy, suggested a U.S. return to the nuclear deal would be needed before Tehran could think of negotiating.