The two-day discussions in Geneva will be followed by a meeting on Wednesday involving the political directors of the other five permanent members of the UN Security Council, Germany and the European Union.
"I can confirm that the talks have begun," the diplomatic source told AFP, without giving further details.
Acting Deputy Secretary of State Wendy Sherman flew in on Monday to lead the US delegation, US officials said, while deputy foreign minister Abbas Araqchi is leading the Iranian side, according to media in that country.
EU negotiator Helga Schmid will also take part in some of the bilateral discussions, ahead of the meeting of the full P5+1 on Wednesday.
The meeting is not set to involve foreign ministers.
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It will be the first time the sides have met since failing to meet a November 24 deadline for a comprehensive deal with Iran on reining in its nuclear programme in exchange for an easing of crippling international sanctions.
The global powers and Iran agreed to give themselves seven more months -- until June 30 -- to strike a deal, although they hope to have the broad outlines hammered out by March.
A final agreement is aimed at ensuring Tehran will never develop nuclear weapons under the guise of its civilian activities.
Iran denies that it is seeking the bomb and insists its nuclear activities are for solely peaceful purposes.