There was no confirmation from Saudi Arabia or Iraq on the resumption of the talks.
"The latest positive meeting has raised hopes for the two countries to take steps toward the resumption of ties,” said Nour News, which is affiliated with the country's Supreme National Security Council. It did not say when the fifth round of talks were held.
Riyadh severed ties with Tehran in 2016 after Iranian protesters stormed the Saudi embassy in the Iranian capital following the execution of a Shia cleric in Saudi Arabia.
Iran suspended the talks in March without giving a reason for the decision that came as a new round of negotiations was due to start. The move came after Saudi Arabia executed 81 men in its biggest mass execution in decades. Tehran condemned the executions that activists said included 41 Shia Muslims.
Predominantly Sunni Muslim Saudi Arabia and Shia Iran, which are locked in proxy conflicts around the region, started direct talks last year to try to contain tensions.
Saudi Arabia and Iran have backed opposing sides in regional conflicts and political disputes in Syria, Lebanon and Iraq for years, and Saudi Arabia has led an Arab coalition waging war against the Iran-aligned Houthi movement in Yemen since 2015.