Before the meeting in Istanbul, Iran also pushed back on suggestions of extending the United Nations resolution that ratifies a 2015 deal, nearing expiry, that was designed to curb its nuclear program.
Delegations from the European Union and so-called E3 group of France, Britain and Germany met Iranian counterparts for about four hours at Iran's consulate for talks that the UN nuclear watchdog said could provide an opening to resume inspections in Iran.
Iranian Deputy Foreign Minister Kazem Gharibabadi said afterwards that both sides had presented specific ideas on sanctions relief and the nuclear issue.
"While seriously criticising their stances regarding the recent war of aggression against our people, we explained our principled positions, including on the so-called snapback mechanism," he said.
"It was agreed that consultations on this matter will continue."
The European countries, along with China and Russia, are the remaining parties to the 2015 deal, from which the US withdrew in 2018. It lifted sanctions on Iran in return for restrictions on its nuclear program.
A deadline of October 18 is fast approaching, when the resolution governing that deal expires.
At that point, all UN sanctions on Iran will be lifted unless the "snapback" mechanism is triggered at least 30 days before.
This would automatically reimpose those sanctions, which target sectors from hydrocarbons to banking and defence.
To give time for this to happen, the E3 have set a deadline of the end of August to revive diplomacy.
Diplomats say they want Iran to take concrete steps to convince them to extend the deadline by up to six months.
Iran would need to make commitments on key issues, including eventual talks with Washington, full cooperation with the UN's International Atomic Energy Agency (IAEA), and accounting for 400 kilograms of near-weapons-grade highly enriched uranium, whose whereabouts are unknown since last month's strikes.
Before the talks, an Iranian foreign ministry spokesperson had said Tehran considered talk of extending UN Security Council Resolution 2231 to be "meaningless and baseless".
IAEA head Rafael Grossi said he was optimistic that nuclear inspection visits might be able to restart this year and that it was important to discuss the technical details now.
"We need to agree on where to go, how to do it. We need to listen to Iran in terms of what they consider should be the precautions to be taken," he told reporters in Singapore.
The United States held five rounds of talks with Iran before its air strikes in June, which US President Donald Trump said had "obliterated" a program that Washington and its ally Israel say is aimed at acquiring a nuclear bomb.
However, NBC News has cited current and former US officials as saying a subsequent US assessment found that while the strikes destroyed most of one of three targeted nuclear sites, the other two were not as badly damaged.
Iran denies seeking a nuclear weapon and says its program is meant solely for civilian purposes.
