Iranian President Hassan Rouhani, shown in June, met with the UK Prime Minister at the United Nations.

Story highlights

NEW: Iran President tweets on "1 hour of constructive & pragmatic dialogue"

NEW: He criticizes U.S.-led strikes in Syria, yet opens door to "a new atmosphere" with U.S.

NEW: Cameron: Despite "severe disagreements," Iranians could help defeat ISIS

NEW: Prime Minister: If they can help, "we should welcome their engagement"

CNN  — 

Leaders from Britain and Iran met Wednesday for the first time in 35 years, a potential breakthrough conversation that occurs at a time when Tehran is trying to shed Western-led sanctions over its nuclear program and Western nations are trying to garner international support for their campaign against ISIS.

Iranian President Hassan Rouhani acknowledged the meeting between him and British Prime Minister David Cameron with a tweet – picture included – from the sidelines of the United Nations General Assembly in New York.

“1 hour of constructive & pragmatic dialogue, new outlook #UNGA,” read his message on the Cameron meeting.

During his U.N. speech later Wednesday, Cameron talked about the meeting, the first since the 1979 Iranian Revolution.

After talking about the need for the anti-ISIS coalition to be “inclusive, engaging the widest possible coalition of countries as possible,” Cameron touched on his conversation with Rouhani.

The two leaders have “severe disagreements,” Cameron said, pointing to “Iran’s support for terrorist organizations, its nuclear program, its treatment of its people. All these need to change.”

Then again, Cameron added, “Iran’s leaders could help in defeating the threat from ISIL,” using a commonly used acronym for ISIS, which calls itself the Islamic State.

“They could help secure a more stable and inclusive Iraq and a more stable and inclusive Syria,” he said. “And if they are prepared to do this, then we should welcome their engagement.”

Cameron’s comments came after the UK mission to the United Nations put out a statement on the meeting, saying the two leaders “agreed that we should seek to progressively improve our bilateral relationship.”

That statement referenced addressing “the future of Iran’s nuclear program.” That remains a focus in Tehran, though the hot topic this week at the United Nations is what to do about ISIS.

ISIS consists of Sunni Muslims aiming to create a vast caliphate in the region under its strict, distinct version of Sharia law. Its advances into neighboring Iraq could pose a threat to Iran, especially given that Iran is made up predominantly of Shiite Muslims.

In fact, Iranian leaders have voiced support for Iraq’s government – which is also led by Shiites – in its fight against the Islamic extremist organization. Brig. Gen. Amir-Ali Hajizadeh even said that members of Iran’s Islamic Revolutionary Guard “stopped” ISIS from entering the Kurdish city of Irbil, according to a report Wednesday from state-run Press TV.

But, in the same story, Hajizadeh ripped the U.S.-led anti-ISIS coalition as part of Washington’s “psychological warfare” policy.

Rouhani on Wednesday criticized the coalition airstrikes in Syria, saying they do not have “any legal standing” because U.N. members haven’t sanctioned them. Iran has been one of the biggest allies of Syrian President Bashar al-Assad, the man who U.S. President Barack Obama and other Western leaders have publicly said they want out of power – even going so far as to support moderate opposition elements fighting to oust him.

Rouhani used rhetorical questions to make his case on Twitter, writing, “Wasn’t DAESH (#ISIS) the same group who fought the Syrian gov & the Syrian army? How is that they were not categorised as #terrorists then?”

Saying that his country never “had doubts or delays in countering #ISIS,” Rouhani tweeted, “Why is it that #ISIS went from not-so-bad to extremely-bad depending on who they had targeted in their #terrorist operations?”

Notwithstanding such criticism and the fact he didn’t meet with Obama in New York, Rouhani didn’t close the door to major changes in his nation’s relationship with its longstanding, often bitter rival, the United States.

“If we are able to reach a #nuclear agreement,” Rouhani tweeted, “a new atmosphere would emerge in US-Iran relations, which I believe would benefit both nations.”