An advisor to President Hassan Rowhani said any talks had to start with Washington returning to the 2015 nuclear deal it abandoned in May.
"Respect for the great nation of Iran, reduction in hostilities, US returning to the nuclear deal... That will open the rocky path of the moment," wrote Hamid Aboutalebi on Twitter.
Trump said on Monday that he was willing to meet ‘any time’ with Iran's leaders without preconditions.
Iran adviser says US talks must include return to nuclear deal
"I would meet with Iran if they wanted to meet," Trump said at a White House press conference, barely a week after he had traded bellicose threats with Rouhani.
But with the US about to reimpose full sanctions, starting on August 6, many in Iran are uninterested in his latest volte-face.
"He must first return to the nuclear deal and implement it before negotiating can even be contemplated," said analyst Mohammad Marandi, of the University of Tehran, who was part of the nuclear negotiating team.
"We cannot negotiate with someone who violates international commitments, threatens to destroy countries, and constantly changes his position," he added.
Others in Iran were more receptive.
"Negotiations with the United States must not be a taboo," said Heshmatollah Falahatpisheh, head of parliament's foreign affairs commission, in an interview with the semi-official ISNA news agency.
"Trump understands that he does not have the capacity to wage war with Iran, but due to historic mistrust, diplomatic ties have been destroyed," said Falahatpisheh, adding that this left no choice but to work towards reducing tensions.
Trump lashes NATO allies as he lands for tense summit
On the streets of Tehran, meanwhile, the focus remained resolutely on domestic problems particularly the collapse of the currency and ongoing economic difficulties.
"Any little thing that can help the people in this bad situation, I really want it to happen for us," said Fathi, a young woman working for an insurance broker.
"All of us believe that Trump is the enemy of Iran and Iranian people. But now maybe Trump wants to give the Iranian people an opportunity and, God willing, it could be a way to get past our disastrous situation," added Hushiar, an office manager in her 50s.
The imminent return of full sanctions has raised fears the country will tip into a major economic crisis, with the currency already losing two-thirds of its value since the start of the year.
Many Iranians find it hard to believe that the man who is trying to destroy their economy, and has banned them from flying to the US, can be trusted.
"If they are honest in their words that they want to have negotiations with us without any preconditions, at least they should stay in the JCPOA (nuclear deal) or they should let us get the benefits of European trade," said Morteza Mehdian, a software engineer in his 20s.
"But the reality is this man is a liar and we cannot trust his word."
Trump seeks to revive 'Arab NATO' to confront Iran
For now, this is also the official line, with supreme leader Ayatollah Ali Khamenei saying earlier this month that talking to Trump would be "useless".
Foreign ministry spokesperson Bahram Ghasemi on Monday said "there is no possibility for talks", ahead of Trump's statement.
"Washington reveals its untrustworthy nature day by day," Ghasemi said, according to the conservative-aligned Mehr news agency.
The Trump administration says it is engaged in a "maximum pressure campaign" designed to force Iran into a new deal that goes beyond limiting its nuclear programme and includes curbs to its regional behaviour and missile programme.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ