Zarif's remarks came as foreign ministers of all six powers were joining the talks as they entered a fourth day in Geneva in the quest for an elusive deal to allay concerns about Iran's nuclear ambitions.
"We have now entered a very difficult stage... That requires the presence of foreign ministers," Zarif told state television.
He arrival of the top diplomats from Britain, China, France, Russia and the United States plus Germany "shows the seriousness of the talks," he added.
"There are narrow gaps, but they are important gaps," said British Foreign Secretary William Hague.
Zarif said his team was insisting on Iran's "rights", saying: "We are not prepared to commit to any (deal) that damages Iran's rights and interests."
A sticking point is Iran's insistence that its "right" to enrich uranium for peaceful purposes be recognised in any deal, even though such a right is not explicitly set out in the nuclear Non-Proliferation Treaty.
"In any agreement, enrichment in Iran will not be suspended," Zarif said, adding that "a very difficult task" still lay ahead in clinching a deal.
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