In draft summit conclusions, the EU was to call on Iran to cooperate fully with the International Atomic Energy Agency (IAEA) "in a spirit of full transparency in relation to its nuclear programme".
But the leaders added: "The European Council stresses the Union's desire to move towards a closer relationship with Iran, on the basis of action by Iran to address the EU's concerns regarding Iran's nuclear programme, the fight against terrorism, human rights, and Iran's approach to the Middle East peace process."
EU heavyweights Britain, France and Germany brokered a deal in October for Iran to give the IAEA a full declaration of all its nuclear activities, giving a green light for tougher inspections by the UN watchdog.
But the deal now appears to be at risk from Iranian intransigence and failure to allay US accusations that Tehran is after more than just civilian atomic power.
Nevertheless, the EU has at the same time stuck to its approach of "constructive engagement" with Iran, in contrast to the United States, which calls the country part of an "axis of evil".