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

STORY HIGHLIGHTS

(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."

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Iran's Rouhani, UK's Cameron have historic, 'constructive' meeting