Russian Foreign Minister Sergei Lavrov told Russian media that global powers had reached "an agreement in principle on all key aspects of the final settlement".
But there was confusion on the status of the negotiations, as ministers from world powers and Iran met deep into the night, working past a March 31st midnight deadline.
French Foreign Minister Laurent Fabius and China's Wang Yi have already left the Swiss lakeside town of Lausanne, though Fabius said he could return if needed.
Washington said there had been enough progress during Tuesday's marathon session to justify pushing past the deadline.
They are grappling for a framework deal — with the complex technical details for a comprehensive accord to be finalized by June 30th — which will stop Iran from acquiring a nuclear bomb.
The stakes are high, with fears that failure may set the United States and Israel on a road to military action to thwart Iran's nuclear drive.
The White House warned again Tuesday that the military option to deprive the Islamic republic of nuclear arms remained open.
If Iran is "unwilling to make those kinds of commitments" that its nuclear programme is peaceful "then we'll have to walk away from the negotiating table and consider what other options may be available to us," said White House spokesman Josh Earnest.
"The military option has been on the table for quite some time and it continues to be . . . on the table," he added.
Lavrov said ministers would start drafting the "agreement in principle," quoted by Ria Novosti.
Iranian Foreign Minister Mohammad Javad Zarif said the talks would resume early Wednesday and he also hoped to start putting down the outlines of the framework.
"The solutions are very clear," he told Iranian television, saying he hoped to begin drawing up the final accord.
A senior US official however said there was not yet full agreement on key points.
"All issues have not been agreed," the official told AFP.
US Secretary of State John Kerry briefed President Barack Obama, and his national security team on Tuesday's negotiations by secure video conference.
Under the final accord, the powers want Iran to scale back its nuclear programme to give the world ample notice of any dash to make the bomb.
In return, the Islamic republic is demanding the lifting of crippling sanctions.
But the question is how much detail will be in the framework under negotiation between Iran and the six powers — the US, China, Russia, Britain, France and Germany.
If it falls short of firm commitments by Iran, Obama will find it hard to fend off attempts by his Republican opponents to pass fresh sanctions on Tehran.
Iran's negotiators are also under pressure from domestic hardliners not to give too much away and for President Hassan Rouhani to deliver on his promises to win the lifting of sanctions.
Fresh US sanctions could torpedo the whole negotiating process launched after Rouhani became president in 2013.
Republicans fear that since some of its nuclear infrastructure will likely stay intact, Iran will still be able to get the bomb — a concern shared by Israeli Prime Minister Benjamin Netanyahu.
"The greatest threat to our security and our future was and remains Iran's attempt to be armed with nuclear weapons," Netanyahu said.
"The agreement being formulated in Lausanne paves the way to that goal."
Other areas of the mooted deal, including the future size of Iran's uranium enrichment capacity also appear to have been tentatively sewn up.
But the two sides still appear to be discussing other areas, including what to do with Iran's stockpiles of nuclear material, and how long the deal should last.