"Tehran has responded positively to (the) UK`s request," the tweet read, saying Rouhani`s meeting with Hague had been "confirmed".
A spokeswoman for the British Foreign Office said a meeting between Hague and Iranian Foreign Minister Mohammad Javad Zarif in New York had long been scheduled, but she was not aware that a meeting with Rouhani was going to happen.
"We set up a meeting with the foreign minister," the spokeswoman said, saying Britain "would be happy" to look at brokering a meeting with the Iranian president too.
Another spokesman added: "We haven`t received any invitation from the Iranians to meet the president, but we wouldn`t exclude it. We do view this as a positive step."
The Foreign Office said any talks with the Iranians would be focused on the Middle East peace process, Syria, and Iran`s contested nuclear program.
British Prime Minister David Cameron has faced repeated calls from the opposition Labour party to try to improve relations with Iran after Rouhani`s election earlier this year.
But while recognizing that Rouhani`s victory was an encouraging sign, Cameron has said relations remain strained, not least because of what he said was the state-backed ransacking by protesters of the British Embassy in 2011.
That incident triggered one of the worst crises between the two countries since the Islamic Revolution in 1979 and resulted in diplomatic ties being downgraded.
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