Iran plans to hold a fourth round of talks with regional rival Saudi Arabia in Iraq after the new Iranian government is set up, the Iranian ambassador in Baghdad was quoted on Tuesday as saying.

Iran and Saudi Arabia, leading Shi'ite and Sunni Muslim powers in the Middle East, have been rivals for years, backing allies fighting proxy wars in Yemen, Syria, and elsewhere. They cut diplomatic ties in 2016.

Iran confirmed publicly for the first time in May that it was in talks with Saudi Arabia, saying it would do what it could to resolve issues between them. Since then, it has elected a new president, hardliner Ebrahim Raisi, who was sworn in on Aug. 5.

The announcement of plans for new talks, carried by the semi-official Iranian news agency ISNA, came days after a regional summit held in Baghdad to help ease tensions among Iraq's neighbors.

"We have had three rounds of negotiations with the Saudi side, and the fourth round is to be held after the formation of a new Iranian government," said Iraj Masjedi, Iran's ambassador to Iraq, according to ISNA.