The comments, made by Pompeo during a press briefing to announce a raft of new sanctions on groups including a unit in the Iran Revolutionary Guards, came just hours after Trump announced his resignation national security adviser and Iranian hawk John Bolton.
Asked about the possibility of a meeting between Trump and Rouhani later this month, Pompeo, speaking alongside Treasury Secretary Steven Mnuchin, said that Trump was "ready to meet without preconditions" . "
Both Trump and Rouhani are scheduled to attend the UN General Assembly in New York in late September.
Mnuchin maintains that even with Bolton out of the picture, the US will continue its "maximum pressure" campaign against Iran. The policy aims to prevent Iran from developing nuclear weapons through economic and military pressure, including sanctions, following Trump's departure from the Iran nuclear deal last year.
Rouhani said last month that there was no meeting until the economic sanctions imposed on Tehran were removed.
Bolton's resignation, which Trump first announced on Twitter on Tuesday, was described by a senior adviser to Rouhani as a "clear sign that the US maximum pressure strategy has failed," according to the state-run Islamic Republic News Agency (IRNA).
"The fact that John Bolton was sidelined and subsequently removed was not an accident," Hesamuddin Ashena said, and predicted "the siege of Iran would be disrupted."
Following Ashena's remarks, Iranian government spokesman Ali Rabiei said the White House's move to oust Bolton would help the Trump administration "better understand the reality of Iran."
"With the expulsion of the largest proponent of war and economic terrorism, the White House will have less obstacles in understanding Iran's realities, "Rabiei wrote on Twitter, according to IRNA. "Months ago John Bolton had promised that Iran would not be there for three months; we were still standing and he was gone."
Bolton was first brought to the administration last year to replace HR McMaster in part because of his hawkish position in Iran – which supports Trump's exit from the Iran nuclear deal and the highest pressure approach. – but soon began to fight the President's vision for diplomacy in North Korea and eventually to Afghanistan.
Bolton maintains that he offered to leave his post voluntarily, tweeting minutes after Trump's announcement, "I offered to resign last night and President Trump said, & # 39; Let's talk tomorrow. '
It is not clear that Bolton's departure was related to Iranian policy. In a tweet on Tuesday, Trump said he "strongly disagrees" with Bolton's suggestions "as did the administration."
White House deputy secretary Hogan Gidley told reporters it was "no issue" that led to Bolton's departure, saying his "priorities and policies were not just aligned with the President. "
But a senior administration official told CNN that Trump is getting annoyed at Bolton for his statements in Iran, Venezuela and Afghanistan. Both disagree with the President's decision to host Taliban leaders at Camp David, many people familiar with the situation told CNN.
Bolton's resignation comes as tensions in Iran escalate in the Persian Gulf, North Korea continues to develop its weapons capabilities, weapons control experts warn of a potential career nuclear weapons with Russia and trade tensions with China intensified, as Trump spoke of a crackdown on Afghan forces.
CNN's Zachary Cohen, Kaitlan Collins, Kevin Liptak and Matt Egan contributed to this report.