Iran's chief negotiator and Supreme National Security Council (SNSC) Secretary Saeed Jalili is leading the Iranian team of negotiators, while delegations of the six world powers are headed by EU foreign policy Chief Catherine Ashton.
The talks are expected to last for two days.
Iran and the Group 5+1 held several rounds of talks in Baghdad last month. The Baghdad meeting came after Iran and the six world powers resumed talks in Istanbul, Turkey, in April.
Both Tehran and the so-called Group 5+1 - comprising UN Security Council permanent members Britain, China, France, Russia and the United States, plus Germany -offered their own packages of proposals at the last round of talks in Baghdad in May.
Iran's package included nuclear and non-nuclear topics such as regional security and the demand that the G5+1 officially recognizes Iran's right to uranium enrichment.
The powers want Tehran to stop enriching uranium to 20 percent fissile purity used to fuel a research reactor in Tehran which produces radioisotopes for medical purposes like cancer treatment.
They put forth a proposal on how to achieve this at a round of talks in Baghdad, in which Tehran would stop production, close the Fordow underground facility where such work is done, and ship its stockpile out of the country.
In return, they offered to supply it with fuel for a medical research reactor in Tehran, which requires 20-percent uranium, and to ease sanctions against the sale of commercial aircraft parts to Iran.
No agreement was reached in Baghdad but the seven countries agreed to continue discussions in Moscow.
Iranian officials have repeatedly reiterated that the country's right to enrich uranium to the level of 20% is Tehran's redline and the world powers should recognize this right in the Moscow negotiations.
Earlier, Iran's Parliament Speaker Ali Larijani said Tehran's nuclear standoff with the West has entered a vital stage dominated by the "war of wills".
"Iran's nuclear issue is at a sensitive juncture and a war of wills has somehow come to dominate it," said Larijani, while addressing a meeting with elites from Iran's Western Hamedan province Saturday night.
"Owing to the very same reason, a correct use must be made of the time" by those involved in Iran's nuclear issue and talks with the world powers, he continued.