The conversation took place in Oman's capital Muscat. It is the first time in several years that the USA and Iran have negotiated at such a high level.
After over two and a half hours of meeting on Saturday afternoon, a motorcade with the American delegation was seen leaving.
The US delegation is led by Middle East envoy Steve Witkoff and the Iranian delegation by Foreign Minister Abbas Araghchi. They sat in different rooms and talked via Omani mediators. But for a few minutes at the end, the envoys were seen eye to eye with Oman's Foreign Minister present.
Next round on 19 April
The talks focused on "sanctions relief and nuclear energy issues" and took place in "a constructive and mutually respectful atmosphere", according to Iran's Foreign Ministry.
"Very positive and constructive", the White House reports.
"These issues are very complicated and special envoy Witkoff's direct communication today was a step forward towards achieving a mutually beneficial result", the White House writes in a statement.
The next round of talks is scheduled to take place in a week, on 19 April.
Abbas Araghchi emphasizes in Iranian TV the importance of achieving results.
Neither we nor the counterpart wants fruitless negotiations, discussions for the sake of discussions, wasting time or talks that drag on indefinitely.
According to Araghchi, the USA wants to reach an agreement on a new nuclear energy deal "as soon as possible".
It will not be easy and it will require a will from both sides, he says.
Only hours before the talks were to begin, US President Donald Trump said that Iranian nuclear weapons are out of the question.
I want Iran to be a wonderful, great and happy country. But they must not have nuclear weapons.
Hoping to lift sanctions
The USA left the previous nuclear energy agreement during Trump's first term. Saturday's surprising talks take place after Trump in March sent a letter to Iran's supreme leader, Ayatollah Ali Khamenei, urging talks.
The pressure on Iran is great. This week, Trump has described military actions against the country as an absolute possibility if the talks do not go in the direction the USA wants, and has even threatened to bomb Iran.
At the same time, Iran wants very clear guarantees that an agreement will hold. The trust in the USA is low and the country hopes that the US-led sanctions against it will be lifted.
