It said on Wednesday that Bolton's exit had not changed that position.
This comes while White House spokesman Judd Deere had said on September 5 that during a conversation with Macron, Donald Trump had stressed that sanctions against Iran will not be lifted at this point.
"The Iranians will be happy that Bolton is fired, but I don't think it's sufficient", Slavin told MEE.
"America should understand that.it should distance itself from warmongers", Iran's semi-official Tasnim news agency quoted President Hassan Rouhani as saying on Wednesday, without mentioning Bolton.
Trump has used sanctions to step up pressure on Tehran since he pulled the United States out of a 2015 deal under which Iran agreed to curbs on its nuclear program in return for a lifting of sanctions.
The $15 billion package would make up for about half of Iran's annual oil sales, the report said, and ease some of the economic pressure on it.
Earlier this year, Trump also blacklisted the Islamic Revolutionary Guard Corps (IRGC), a branch of the Iranian military, as a terrorist group.
Cruz tweeted that he hoped Bolton's departure "does not mean that the deep-state forces at State and Treasury - who have been fighting tooth and nail to preserve the Obama Iran nuclear deal - have finally convinced the president to go soft on Iran". He was sacked the next day.
At the center of the tension between Trump and Bolton is a difference in ideology. You look at so numerous things that are happening.
In an effort to protect the nuclear deal, France has proposed giving Iran a multi-billion dollar credit line which would shield it from some of the impact of USA sanctions, although any such deal would require the Trump administration's tacit approval.
"Even if Trump is willing to do some kind of sanctions-relief or reduce sanctions, the key thing is that it has to materialise before any kind of meeting sit-down or negotiations", Toossi told Middle East Eye.
Last year, the United States pulled out of an worldwide agreement between Iran and world powers under which Tehran accepted curbs on its nuclear programme in return for access to world trade.
"It's too late for the UNGA", he said.
He added: "From the point of view of the government, parliament and the people of Iran there is no point in negotiating with the United States while the sanctions are still in place". For one, the maximum pressure campaign has gone nowhere, and it has pushed Iran out of compliance with the nuclear accord. "We may be seeing a shift now".
Critics say the pressure campaign dangerously brought the two countries to the verge of a military confrontation this summer. At different times, Trump sought to test diplomatic options with each country, but Bolton aggressively resisted the moves, officials said.
Joe Macaron, a fellow at the Arab Center Washington DC, said both sides should seize the opportunity created by Bolton's firing. Where will Bolton's departure cause changes?
Trump is mulling easing sanctions on Iran as a way to increase the odds of a face-to-face meeting with Iranian President Hassan Rouhani.
Reporting from Tehran, Al Jazeera's Dorsa Jabbari said the Iranian officials "don't really see a major change" in the USA policy towards Iran with the departure of Bolton, who was one of the strongest advocates of a hard line towards the Middle Eastern country.