David Cameron is to hold the first bilateral talks between a British prime minister and an Iranian president since the 1979 revolution when he has a face to face meeting with President Hassan Rouhani in the next two days in New York.

The meeting, a significant thaw in diplomatic relations between the countries, is designed to explore the support the Iranians can give to the fight against Islamic State (Isis) in Iraq and Syria.

The Iranians were not allowed to attend the recent Paris talks on building an international coalition against Isis, and have also been excluded from all talks about dislodging President Bashar al-Assad in Syria, including the two conferences in Geneva.

Rouhani has been a fierce critic of Isis, but has derided the US air strikes campaign as it involves no commitment to ground forces.

Cameron is expected to make clear that Isis is a common and extremely serious threat that can only be tackled in Iraq and that Iran must drop its support for President Assad, who, in the words of Downing Street, has “created the conditions that have allowed terrorism to flourish”.

Cameron will also send a tough message to the Iranians on the long-running nuclear negotiations on behalf of the E3 + 3 group that: “Iran has a rare opportunity to embolden its prosperity through a deal but this is only possible if Iran is willing to show flexibility and be realistic about the future scope of its nuclear programme, in particular the issue of enrichment.”

No 10 sources said: “We are under no illusion about the dangers of Iran’s nuclear programme and our approach on that is not changing. However, if Iran is willing to join the international community to defeat Isis then we will work with them on that, but will be clear you cannot take one approach in Baghdad and another in Damascus. You need a political solution in both if you are serious about defeating Isis.”

Speaking to NBC News from the presidential palace in Tehran before his visit to the UN, Rouhani questioned Barack Obama’s decision to go after Isis with air strikes.

“Are Americans afraid of giving casualties on the ground in Iraq? Are they afraid of their soldiers being killed in the fight they claim is against terrorism?” Rouhani said.

“If they want to use planes and if they want to use unmanned planes so that nobody is injured from the Americans, is it really possible to fight terrorism without any hardship, without any sacrifice? Is it possible to reach a big goal without that? In all regional and international issues, the victorious one is the one who is ready to do sacrifice.

“Maybe it is necessary for air strikes in some conditions and some circumstances,” he added. “However, air strikes should take place with the permission of the people of that country and the government of that country.”

No 10 said Cameron will also hold talks with Egyptian president Abdel Fattah el‑Sisi on Tuesday. He will say the UK wants to work with Egypt in the region, but can only do so when there are inclusive governments, strong institutions, safeguards for minorities and respect for human rights.

He will also use his visit to speak to US business executives in New York to launch a campaign for transatlantic prosperity through the conclusion of the elusive EU-US trade deal in 2015.

The prime minister will speak at the UN climate summit on Tuesday.

The summit is trying to lay the groundwork for a global deal on climate change in Paris next year designed to keep the international community committed to a target of preventing the world warming by more than 2C.

Cameron will insist each country should be allowed to make its own decision on energy promises, so long as they set overall carbon targets.

As part of the talks the prime minister will say the EU is planning to offer an emissions cut of 40%.

No 10 sources said: “We have got to go further in terms of explaining how tackling climate change is not simply a green policy – it’s a growth policy. If you are going to get the world economies to stick to the 2C target you have got to be serious about cutting green tape and creating green jobs.”