"We cannot miss this opportunity," Federica Mogherini, whose predecessor Catherine Ashton chairs the talks in Switzerland, said at Chatham House, a think tank in London.
"A good deal is at hand if the parties will keep cooperating as they did so far and if we have enough political will from all sides to agree on a good deal and sell it domestically," Mogherini said.
"We have a series of internal domestic political dynamics we have to handle with care," she said, listing "tensions" in the US Congress, Israel's elections and Sunni-Shiite rivalry in the Gulf region.
US Secretary of State John Kerry earlier today said world powers "had made inroads" since reaching an interim deal with Iran in November 2013 on reining in its suspect nuclear programme.
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"We expect to know soon whether or not Iran is willing to put together an acceptable, verifiable plan," Kerry said after returning from talks in Geneva with his Iranian counterpart Mohammad Javad Zarif.
The so-called P5+1 group of Britain, China, France, Russia, the United States and Germany are trying to strike an accord that would prevent Tehran from developing a nuclear bomb.