"It is over for today," the source said, adding that the agenda for Monday is not clear yet.
Earlier, another source told RIA Novosti that talks "may continue all night."
The source added that Iran's head of Iran's Atomic Energy Organization Ali Akbar Salehi and US Energy Secretary Ernest Moniz are also taking part in the dialogue.
The plenary session of the P5+1 was held earlier on Sunday at the EU mission on Geneva. A source in one of the delegations has earlier said that experts-level meetings to work on technical issues will be held on Monday.
Delegates from Russia, China, France and Germany, the remaining P5+1 group members, also took part in talks at the EU mission Sunday evening.
Suspicious that Tehran is developing nuclear weapons, the UN Security Council and a number of countries have handed down a series of sanctions on Iran. Meanwhile, Tehran maintains its uranium enrichment program is for peaceful purposes only.
Several rounds of P5+1 format talks have been held in the past, and the current deal requires a long-term comprehensive agreement on Iran's contested nuclear program to be reached by the end of July 2015.