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Others say the departure of Bolton, an advocate of "regime change" in Iran who has repeatedly called for bombing the country's nuclear facilities, increases the likelihood of a compromise from the Trump administration.
Secretary of State Mike Pompeo and Treasury Secretary Steven Mnuchin stressed the United States would maintain its campaign of "maximum pressure" against the Islamic republic.
But Mr. Pompeo's personal rapport with Mr. Trump, his willingness to defend the administration in the media and his determined campaign never to show daylight between himself and the president on major issues are likely to take on new significance with Mr. Bolton gone.
He spoke at a cabinet meeting in Tehran.
And that relates to some criticism that I heard all day today, is that Bolton tries to persuade the president, rather than present options that all of the agencies have, as the National Security Council is created to do.
"The Americans must understand that they will not benefit from bellicosity and warmongering".
Rouhani's website quoted him as urging the U.S. to also abandon the "maximum pressure policy" on Iran.
Rouhani, in a phone call with French President Emmanuel Macron later Wednesday, repeated his position that if Europe finalizes a way for Iran to sell its oil, Iran would return to the nuclear deal's commitments.
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"As long as the USA government's economic terrorism and such cruel sanctions are imposed on the Iranian people, there is no room for negotiations", he was quoted as saying by state news agency IRNA.
Opinions vary on what Bolton's departure will mean for USA policy toward Iran.
Now the Washington-based member of the team is out of the picture - and Zarif said on Wednesday that "the world. was breathing a sigh of relief over [the] ouster of #B_Team's henchman in the White House".
"The enemy imposed "maximum pressure" on us".
"It's too hard to say if a meeting will happen given the question of whether it's politically palatable for both leaders", Bloomberg quoted Kupchan.
Ali Shamkhani, a top Iranian security official and secretary of the Supreme National Security Council, said Bolton's exit has "no impact" on how Tehran views USA policy.
National security sources said Tuesday that Mr. Bolton's departure could open the way for renewed "working level" talks with North Korea - an approach the State Department pursued only to be shut down by Mr. Bolton's demand that Pyongyang accept an all-or-nothing deal.
The fractious relationship between Bolton and Trump has always been demonstrated in their disagreements over worldwide policy.
However, the ambassador said in an interview with Iran's state media that there is no room for dialogue with the USA as long as Washington's "unfair" sanctions and "economic terrorism" against Iranian people continue.
The deal put forth by France would compensate Iran for oil sales disrupted by American sanctions.