"Senior officials from the secretariat of Iran's Supreme National Security Council (SNSC) and the head of the Saudi intelligence service" attended a meeting, Nour News said of the talks.
"The latest positive meeting has raised hopes for the two countries to take steps toward the resumption of ties,” added Nour News, which is affiliated with the SNSC. It did not say when the fifth round of talks were held.
"Talks resumed last Thursday in Baghdad," the official told AFP, speaking on condition of anonymity, and without giving further details.
The talks in Iraq – which borders both Iran and Saudi Arabia – are the fifth round of meetings in the country in the past year between Tehran and Riyadh aimed at restoring ties.
Saudi Arabia cut diplomatic ties with Iran in 2016 after protesters stormed Saudi diplomatic missions in Tehran and Mashhad in the aftermath of the kingdom’s execution of revered Shia cleric Nimr al-Nimr.
"It is expected that a joint meeting between the foreign ministers of the two countries will be held in the near future," Nour News said.
In March, Iran had suspended participation in talks after Saudi Arabia announced it had executed in just one day a record 81 people convicted of various crimes related to "terrorism", including men linked to Yemen's Ansarullah movement.
Tehran condemned the executions that activists said included 41 Shia Muslims, Reuters wrote.
But in early March, Saudi Crown Prince Mohammed bin Salman said his country and Iran were "neighbors forever", and that it was "better for both of us to work it out and to look for ways in which we can coexist".
The comments were welcomed by Iran's Foreign Minister Hossein Amir-Abdollahian.
"We have different views and approaches on some issues in the region, but the management of differences by the sides can serve the interests of the two nations," Amir-Abdollahian said at the time.