Diplomats, however, said that the talks would be tough and might still fail, after supreme leader Ayatollah Ali Khamenei's warning that he would not be retreating one step from the rights of the Iranian nation. (Agencies)
"Considerable gaps remain," a senior Western diplomat said in Geneva after Wednesday's initial meetings.
A second was more upbeat, "I am not saying it's in the bag but we are in a process that started well and which could lead to a deal this weekend."
Numerous attempts to resolve the standoff have failed over the last decade, but the election this year of Hassan Rouhani as president has raised hope that this time a deal can be struck.
With the country reeling from sanctions, since taking office in August Rouhani has put the brakes for the first time in years on expanding Iran's atomic activities.
The United States, Russia, China, Britain, France and Germany, the P5+1, now want Iran to suspend certain parts of its nuclear programme for several months.
In return Iran is being offered minor sanctions relief, although officials insist that core sanctions on its oil exports and banks will stay in place. Over subsequent months a final deal would be worked out.
On Wednesday US Secretary of State John Kerry sought to reassure skeptics at home and in Israel worried that Iran would still be left with the capability to make a nuclear bomb.
"We will not allow this agreement, should it be reached to buy time or to allow for the acceptance of an agreement that does not properly address our core, fundamental concerns," Kerry said in Washington.
Israel though, which has refused to rule out bombing Iran and which is assumed to have nuclear weapons itself, wants a total and permanent dismantlement of Tehran's nuclear facilities.
"Such a deal may have been possible in 2005 when Iran had fewer than 300 uranium centrifuges enriching uranium at one site," Daryl Kimball from the Arms Control Association said.
Diplomats, however, said that the talks would be tough and might still fail, after supreme leader Ayatollah Ali Khamenei's warning that he would not be retreating one step from the rights of the Iranian nation.