The talks are being coordinated by EU foreign policy chief Catherine Ashton, and her spokesman, Michael Mann, said the two sides are "getting down to the nitty-gritty" in discussions scheduled to adjourn Friday, about two months before the July 20 target date for a deal.
The United States and its allies hope to reduce Iran's potential nuclear weapons-making capacity by negotiating substantial cuts in its atomic programme. Tehran says it has no interest in such weapons but is ready for some concessions if all sanctions on its economy are lifted.
The diplomats demanded anonymity because they are not authorized to discuss the confidential talks. But they gave a partial picture of where things stand.
Areas of progress include the partially built reactor at Arak was meant to be a heavy-water facility that would produce substantial amounts of waste plutonium - material that can be used as the core of a nuclear weapon. There is tentative agreement on re-engineering the reactor to a light-water installation or cutting back on its output.
Major differences remain on uranium enrichment.
Iran now has nearly 20,000 centrifuges set up, with about half of them producing uranium enriched to reactor fuel-grade levels. Iran says it is enriching only for peaceful purposes but if reconfigured, the centrifuges could produce weapons-grade uranium for nuclear bombs.
The United States, Britain, France and Germany say no more than a few thousand of the machines should be left standing. Tehran wants to expand the programme, or at least keep the status quo.
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