Tehran and Riyadh, which severed diplomatic ties in 2016, held four rounds of talks in Iraq between April and September last year, with a fifth meeting last Thursday.

"The fifth round of negotiations between Iran and Saudi Arabia in Baghdad ... was positive and serious and saw progress," foreign ministry spokesman Saeed Khatibzadeh told reporters.

Shiite Muslim-majority Iran and the Sunni kingdom of Saudi Arabia support rival sides in several conflicts, including in Yemen, where Tehran backs the Huthi rebels and Riyadh leads a military coalition supporting the government.

In 2016, Iranian protesters attacked Saudi diplomatic missions in the Islamic republic after the kingdom executed revered Shiite cleric Nimr al-Nimr. Riyadh responded by cutting ties with Tehran.

Iran's Nour news agency reported the latest talks were attended by "senior officials from the secretariat of Iran's Supreme National Security Council and the head of the Saudi intelligence service".

It added that the foreign ministers of the two countries were expected to meet "in the near future".

Khatibzadeh said that "if the negotiations are upgraded to first-class political level, it can be expected that progress can be made swiftly in different sectors of the talks".

The spokesman also said "an agreement was reached to hold the next round of negotiations" between Iran and Saudi Arabia, but he did not specify a date.