The leader of Iran's reformist movement, Mohammad Khatami, has urged the west to show courage and work with President Hassan Rouhani or risk losing an unprecedented opportunity to end the current standoff.

In an article published in the Guardian today, Khatami, a former president of Iran, said on the eve of Rouhani's eagerly anticipated visit to the UN that the moderate cleric had "the necessary authority" for a diplomatic resolution to the longstanding differences between Tehran and the west, not least on the nuclear issue. He warned that failure would strengthen extremists on both sides.

Speaking before leaving Tehran for New York , Rouhani pledged to revamp Iran's image, which he said had been distorted. But he fell short of blaming his predecessor, Mahmoud Ahmadinejad, who delivered anti-western tirades each time he spoke at the UN.

Rouhani is scheduled to deliver his speech a few hours after Barack Obama's welcoming statement on Tuesday, amid speculation that the first face-to-face encounter between leaders of the two countries since the 1970s will take place. Rouhani will also be accompanied on his visit by Iran's only Jewish MP.

The EU's foreign policy chief, Catherine Ashton, who met Iran's foreign minister, Mohammad Javad Zarif, on Monday in New York to talk about the country's nuclear programme, described her discussions as constructive. According to Ashton, Zarif and the US secretary of state, John Kerry, will meet on Thursday in what will become the first ministerial talks between Tehran and Washington since the Islamic revolution in 1979.

Britain's foreign secretary, William Hague, met Zarif for the first time on Monday night and discussed the nuclear issue and Syria. They also talked about the prospect of gradually restoring full diplomatic relations between the UK and Iran, which were severely damaged when the British embassy in Tehran was over-run by a mob in November 2011. Hague made clear Britain required solid guarantees from Tehran that its diplomats could operate in safety.

"We don't want a confrontational relationship with Iran," Hague said after the meeting with Zarif.

"We have discussed how to improve our bilateral relations but it will have to take place on a step-by-step basis. I think we are agreed on this. So we have asked our officials to some work on this. Ultimately for Britain to be able to operate an embassy in Tehran again, we would have to know that the embassy could perform all the normal functions of an embassy without harassment and difficulties that it had to face before."

British officials said that no further meetings had been scheduled but that British and Iranian diplomats would be meeting in the coming weeks to discuss how to re-establish confidence in Tehran's intentions.

Khatami, meanwhile, is throwing his weight behind Rouhani in the hope that lessons are learned from missed opportunities under his own presidency.

"For the first time there is an opportunity to create a national consensus above and beyond partisan factionalism, which may address the political predicaments of the country with an emphasis on dialogue and mutual understanding globally," Khatami writes in his first article published in a foreign newspaper.

According to Khatami, Rouhani enjoys backing from all segments of Iranian society in his bid to pursue "constructive engagement" with the west, including from the supreme leader, Ali Khamenei, who has shown some softening in his views about diplomacy recently.

In a further move to boost Rouhani's credibility at the UN, Khamenei on Monday declared an amnesty for 80 political prisoners, including many arrested in the aftermath of the disputed 2009 election.

Khatami's intervention comes as 500 prominent Iranian intellectuals and activists wrote to Obama, telling the American president that it is now his turn to reciprocate.

Signatories to the letter – also published exclusively by the Guardian – include the Oscar-winning film director Asghar Farhadi, the imprisoned reformist Mostafa Tajzadeh and the prominent intellectual Saeed Hajjarian.

"The people of Iran seized the opportunity to elect Hassan Rouhani … as a result, we have witnessed the release of several political prisoners and relative progress in the country's public and political atmosphere," the letter says.

"It is now your turn, and that of the international community, to reciprocate Iran's measures of goodwill and pursue a win-win strategy that encompasses the lifting of the unjust economic sanctions on Iran."

At least 88 of the signatories are former or current political prisoners, some still serving lengthy prison terms. Mohammadreza Jalaeipour, a former political prisoner who was behind the letter, said if Rouhani meets Obama, it will pave the way for a positive change in Iran's internal political atmosphere.

He said: "This letter … says with a loud voice that Rouhani has the support of reformists and those seeking for democracy in Iran."

Hajjarian, who was the target of an assassination attempt in March 2000, echoed Jalaeipour, saying sanctions have hurt the quality of ordinary people's lives in Iran. "The US has not yet realised the changes that have been taking place after people's vote [for Rouhani]," he told the Guardian.

Under Khatami's administration between 1997 and 2005, Iran opened up towards the west, even helping American forces in Afghanistan, but was nevertheless labelled a part of the "axis of evil", along with Iraq and North Korea, by George Bush. Khatami's support was crucial in Rouhani's sensational victory in the June election.

In his article, the ex-president warns that diplomatic mistakes now will have consequences beyond Iran's borders later. "Failure now to create an atmosphere of trust and meaningful dialogue will only further boost extremist forces on all sides. The consequences of such a failure will not only be regional but global," Khatami writes. "For a better world, not only for the Iranian people but for the next generation across the globe, I earnestly hope that President Rouhani will receive a warm welcome and meaningful responses during his visit to the UN."

Sadeq Zibakalam, a Tehran University professor and one of the signatories of the letter, said different factions within the Iranian establishment, including fundamentalists, had come to the conclusion that Iran needed a rapprochement with the US: "They have realised that without this, they can't bring changes to Iran's current dire situation, especially its economy."

Zibakalam warned that if Rouhani fails to engage with the US, "his position in Iran will be significantly weakened" and he will have a hard time in the next four years.

Iran's currency significantly recovered against the dollar on Monday, rising to its strongest value in several months. Expectations of a Rouhani-Obama meeting come as a poll commissioned by the international civic organisation Avaaz, was released showing strong support both in the US and in Iran for an improvement in bilateral relations. It showed that, of those who expressed an opinion, 74% of Americans and 80% of Iranians support direct talks.