Iran has insisted that Heinonen's visits to Tehran are part of its routine cooperation with the International Atomic Energy Agency (IAEA) but the watchdog has said they are focussed on the weapons claims.
"These talks will probably last three days and their first round will start today (Monday) afternoon," Iran's ambassador to the IAEA, Ali Asghar Soltanieh, was quoted as saying by the Fars news agency.
Heinonen had held closed-door talks with Iranian officials in Tehran on April 21 and 22.
The IAEA said on Wednesday that Heinonen reached an agreement with Iran to examine the allegations Tehran has studied how to design nuclear weapons. The claims stem from intelligence provided to the IAEA by some member states.
But Iranian officials have repeatedly played down the links between Heinonen's visit and the so-called weaponisation studies. Tehran has not confirmed the existence of the new agreement.
"This session too is like other normal meetings that deal with technical and expert discussions under the framework of the agency's statute and the nuclear Non-Proliferation Treaty," Soltanieh said of the new talks.
"If there are any questions or ambiguities, we will give the necessary answers away from political fuss," said Soltanieh, who is heading the Iranian delegation in the talks.
The ISNA news agency reported that Heinonen arrived in Tehran earlier on Monday.
In a closed-door briefing to diplomats at IAEA headquarters in Vienna on February 25, Heinonen presented detailed information suggesting that Iran could have been studying how to use its nuclear technology to make a warhead.
Iran, which insists its nuclear programme is entirely peaceful and aimed solely at generating energy, furiously denounced the presentation as fake.
