In Tehran's power circles, where Death to America is regularly chanted, the idea that Iran should eventually negotiate with President Trump, according to several people with knowledge of the change, is being adopted.
These people said the Iranian leadership had concluded that Mr Trump could be re-elected and that the country could not withstand another six years of the severe sanctions it imposed.
This is a remarkable twist on the political establishment in Tehran, which for the past 40 years has set its legitimacy against the United States, but has been particularly hostile to Mr Trump.
Mr. Rouhani turned around within 24 hours, suggesting that he may have been rejected by Iran's supreme leader, Ayatollah Ali Khamenei. But people familiar with the thinking of the Iranian hierarchy said that Mr Rouhani's behavior should be seen as part of the emerging new strategy.
They stated that the strategy followed two parallel traces: showing a more challenging stance on Iran's military and nuclear energy policies that annoyed Mr Trump while signaling his readiness to speak under certain conditions, appealing to what is seen as the instincts of his party to the transaction.
"Iran is completely displaced," said Abbas Abdi, a concurrent leader of students who took hostages at the United States embassy in 1979 and a prominent figure in a faction known as the Reformers, which was open to dialogue with the Americans.
Difficult people who oppose such dialogue, said Mr Abdi. , "He concluded that what works with America now is difficult, but open to talks if Trump offers some guarantees."
Iranian leaders were predictably outraged last year after Mr. Trump abandoned Iran's nuclear a 2015 agreement with the world powers calls for a tougher agreement and restores crippling sanctions against Iran.
Although some may have hoped that Mr. Trump would be fired as a one-time president, this view is fading.
the strategy, those who spoke of it, was also predisposed to debunking Mr Trump's foreign policy victory, which he could use to bolster his re-election prospects.
In early August, First Vice President Ashak Jahangiri met with a group of advisers and political partners to discuss the government's approach to relations with the United States, according to one person who attended the meeting and another who knew about it.
If Mr Trump wants a "more comprehensive" deal than the existing agreement, then Iran will consider his request – and even discuss parts of his ballistic missile program and Iran's role in the region – but in return, Iran will asked for a fuller guarantee from the United States d States for long-term economic relief, people said during the meeting.
"This golden window of opportunity is unlikely to be repeated in the next decade," Sade Alhuseni, senior foreign and economic advisor to Mr. Jahangiri, said in a Twitter message. "This is the beginning of the game for Iran. The upcoming US election gives Iran a rare card to play with Trump. "
The" maximum pressure "campaign put forth by Mr. Trump did not threaten to overthrow the Iranian government or lead to a popular uprising, as some government critics had hoped. But growing tensions with the US carry the risk of military conflict, which Mr Trump says he wants to avoid.
Signs of Iran's strategy for relations with Mr Trump have become clearer in recent weeks.
Iran has taken down a drone, seized a British tanker, revealed an improved missile defense system and exceeded the amount of enriched uranium allowed under the nuclear agreement.
As part of the strategy, people who know about it say Iranians intend to escalate tensions even further over the next few months to strengthen their hand in potential talks.
Iran is expected to announce further exclusion from the nuclear deal by the first week of September, and Iranian officials have said they could increase uranium enrichment by up to 20 percent, far higher than needed for civilian use.
At the same time, Iran has stepped up diplomacy. Foreign Minister Mohammad Javad Zarif toured Europe, stopped at a Group 7 summit by surprise invitation from France and traveled to China, Japan and Malaysia to meet with the heads of state.
Mr. Trump did not meet with Mr Zarif during the Group 7 gathering, and it remains unclear what the Iranian foreign minister might have wanted there. But Iranian analysts said Iranian analysts were almost certainly promoted.
"The Iranians are in a deep economic crisis and there is only one way out," said Nader Hashemi, director of the Middle East Center at the University of Denver. "They will try to force the deal to be as sweet as possible."
Mr. Zarif's statement heightened speculation about direct talks after French President Emmanuel Macron announced on the sidelines that Mr Trump and Mr Ruhani could sit down within weeks.
Mr. Trump did not give any indication at the summit that lifting or suspending sanctions was on the table, but he said other countries could give Iran a line of credit for oil to "get them in a very rough folder."
On the part of Mr. Rouhani, even as he rejected the upcoming meeting with Trump, he offered a conditional opening.
"We will not make a positive change in our relations with the US without America ending sanctions and correcting its mistakes," Mr. Ruhani said on Tuesday.
Opponents of such a meeting in both countries remain vocal, reflecting the history of mistrust shaping relations since the 1979 Islamic Revolution.
After Mr Ruhani reached the opportunity to meet Mr. . Trump, Caihan, a Tehran newspaper who is a mouthpiece for the hard factions, asked, "Are you crazy?"
United against nuclear Iran, a New York-based group that supports the rejection of Trump by nuclear forces, sai d, "The momentum created by maximum pressure can quickly evaporate if the negotiations between the United States and Iran are premature."
The ultimate decision on whether to negotiate with Mr. Trump is with Ayatollah Khamenei. Iranian analysts and politicians said Mr Zarif would not be sent to the Group 7 meeting without Ayatollah Khamenei's approval.
While Ayatollah Khamenei has always attacked the United States, he has in the past shown flexibility when all opportunities have been exhausted if a compromise on saving individuals for Iran can be reached.
Iranian analysts and politicians cited three examples where the government turned and put itself under unbearable pressure: the release of US hostages in 1981, the United Nations' resolution to end the eight-year war with Iraq in 1988, and the nuclear one. deal with Iran in 2015
Ayatollah Ruhollah Khomeini, the father of the Islamic Republic, said stopping the war with Iraq was "more deadly than taking poison. "The expression 'glass of poison' has since become synonymous with Iran for capitulation. ("Displaying heroic flexibility" was the term preferred by Ayatollah Henai after the nuclear deal.)
Iranian politicians and analysts say hostage talks with the United States since 1981 are being studied as a potential precedent for discussions with Mr. Trump .  At that time, which also coincided with the presidential election season, Iran agreed to release the hostages with the administration of President Jimmy Carter, but delayed their release, denying Mr. Carter an achievement that could have helped him win re-election. Hostages are released as President Ronald Reagan gives his opening address.
"The rhetoric you hear against talking to America is part of the tactic," said Said Sharia, leader of the political Iranian reformer party. "Iran and the US will never solve their problem completely, but they have made concessions before and will have to do it again."