With the departure of President Trump's National Security Adviser John Bolton, the top tier of the U.S. government lost a long-time hawk on Iran. Bolton has advocated a tough stance on the Islamic Republic for decades, endorsing a preemptive strike to destroy the country's nuclear program as he filled posts from the White House to the United Nations.

As the dust from his resignation settled early Wednesday morning, analysts saw reason to hope for a slight easing of the tension, but little chance of any sudden breakthrough in the nuclear standoff that has stoked fears of a new war in the Middle East.

"The departure of U.S. National Security Adviser John Bolton from President Donald Trump's administration will not push Iran to reconsider talking with the U.S.," Iranian state-run news agency IRNA quoted the Islamic Republic's envoy to the United Nations as saying on Wednesday.

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Abassador Majid Takht-Ravanch reiterated Iran's insistence that direct dialogue with the U.S. government was not possible unless sanctions imposed by the White House were lifted.

President Trump hit Iran with a raft of harsh economic sanctions soon after pulling the U.S. out of the international Iran nuclear deal forged in 2015. The Trump administration has called it a "maximum pressure" campaign to force Iran to renegotiate the terms of the deal, which the president has lambasted as being far too generous to Iran.

Secretary of State Mike Pompeo said Tuesday, after Bolton resigned, that he could envision a meeting between Mr. Trump and Iranian President Hassan Rouhani during the United Nations General Assembly, which begins next week.

"The president has made it clear he's prepared to meet with no pre-conditions," Treasury Secretary Steven Mnuchin said Wednesday, speaking alongside Pompeo.

But the line from Tehran's U.N. ambassador suggested the Iranians intend to stand by their own precondition — no talks until the sanctions imposed by Mr. Trump's administration are lifted. In the end, like all other decisions in Iran, it will be for Supreme Leader Ayatollah Khamenei to determine whether Rouhani meets Mr. Trump in New York.

Rouhani himself weighed in on Wednesday to say the U.S. should "abandon warmongering and its maximum pressure policy," hinting at approval of Bolton's departure, and government spokesman Ali Rabiei said the change in Washington could lead to a "less biased" stance from the Trump administration.

But Iranian Foreign Minister Javad Zarif, who has been sanctioned by the Trump regime personally, pointed to an expansion of U.S. counterterrorism powers on Tuesday, granting the Treasury more power to sanction groups associated with terror organizations, as a "further escalation of #EconomicTerrorism against Iran."

As the world—minus 3 or 2 panicked cohorts—was breathing a sigh of relief over ouster of #B_Team's henchman in the White House, Pompeo & Mnuchin declared further escalation of #EconomicTerrorism against Iran. Thirst for war—maximum pressure—should go with the warmonger-in-chief. pic.twitter.com/im8gXJIxEn — Javad Zarif (@JZarif) September 11, 2019

Iran was infuriated last year by the Trump administration's move to designate the country's elite Revolutionary Guard a terrorist group.

Sir Richard Dalton, a former British Ambassador to Iran, told CBS News on Wednesday that Bolton's departure "improves the odds slightly on an easing of the U.S. maximum pressure campaign."

He said it could also give more room for French-led efforts to give European nations a way of working around the U.S. sanctions, to enable Iran to continue selling some of its oil. That, Dalton said, could serve "as a prelude to multilateral talks."

But the former ambassador said he saw little sign of willingness from Iran or the Trump administration to take meaningful steps back from their entrenched positions.

Iran "would go back to the JCPOA (2015 nuclear deal)," Dalton said, "but is not going to be offered the chance within a U.S. context."

Dalton said it was possible the French-led multilateral efforts to ease tension with Iran could bear fruit, but only if the "current digging-in in both Washington and Tehran were to give way to pragmatism."

"As I read the situation, neither Tehran nor Washington is in a hurry to try a new tack: they have not given up on their underlying positions," Dalton said.

Cliff Kupchan, a former State Department official who now chairs the Eurasia Group risk consultancy, seemed to agree that animosity could ease, but saw no reason to expect a sudden, dramatic change.

"Bolton has been 'Dr. No' when it comes to talks with Iran," Kupchan wrote in an analysis quoted widely by financial news outlets.

He said it was "probably still unlikely" the Ayatollah would approve a Trump-Rouhani meeting, but suggested there was now more "upward pressure on the chance of a meeting."

"Moreover, the former NSA was a key proponent of the aborted strike on Iran and of regime change there," Kupchan noted. "The chance of U.S. strikes on Iran, all else equal, also goes down with his departure."

President Trump said Tuesday that he would name a new NSA "next week."