Iranian President Hassan Rouhani did not refer to John R. Bolton by name but did seize on the ouster of the Trump administration’s hawkish national security adviser to make headlines Wednesday.

“The U.S. should understand that warmongering and warmongers have no benefit and the warmongers should be set aside,” Mr. Rouhani told a government meeting in Tehran, according to Iranian state-media reports that did mention Mr. Bolton’s dismissal a day earlier.

Other Iranian officials sought to downplay the notion U.S.-Iran tensions will be eased by Mr. Trump’s firing of Mr. Bolton, who was widely seen as the administration’s most aggressive Iran hardliner because he once advocated for regime change in Tehran.

Iran’s FARS News Agency cited Abbas Ali Kadkhodayee, a spokesman for the Islamic republic’s “Guardian Council,” which oversees the vetting of people allowed to run for office in the country, as saying Tehran does not believe it is likely Washington’s policies will change because of Mr. Bolton’s ouster.

“The U.S. hostile and arrogant policies do not change by one person’s dismissal,” Mr. Kadkhodayee was quoted as saying via Twitter. He continued, “John Bolton’s ouster shows failure of Trump’s policy of pressure and admission of the fact that warmonger Bolton had closed his eyes on realities.”

Trump administration officials, including Secretary of State Mike Pompeo, have shown no sign of easing their “maximum pressure” campaign of increased sanctions and an oil embargo against Iran. The White House has heaped such pressure against Tehran in the wake of Mr. Trump’s withdrawal last year from the 2015 international nuclear deal with Iran.

The deal had given sanctions relief to Iran in exchange for limits to Iran’s nuclear programs. Mr. Pompeo and others in the Trump administration have said their goal now is to pressure Iran into a new negotiation that addresses issues beyond the Islamic republic’s nuclear activities, such as Tehran’s ballistic missile program and its backing of militant proxies around the Middle East.

However, during the hours after Mr. Bolton’s firing on Tuesday, Mr. Pompeo indicated that Mr. Trump remains open to direct talks with Iran, without any preconditions.

When asked by a reporter whether there could be a meeting between Mr. Trump and Mr. Rouhani on the sidelines of the U.N. General Assembly meeting in New York later this month, Mr. Pompeo said: “Sure.”

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