DUBAI, Aug 31 (Reuters) - 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 neighbours. read more "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. Iran’s parliament last Wednesday approved all but one of the nominees for a cabinet of hardliners presented by Raisi. read more Separately, Iran"s foreign minister said he had discussed ways of improving ties during a meeting with Vice-President Sheikh Mohammed bin Rashid al-Maktoum of the United Arab Emirates on the sidelines of the Baghdad summit. "In this conversation, we talked about the positive intentions and will of the two countries" leaders to strengthen relations... Working with neighbours is the (new Iranian) government"s priority," Foreign Minister Hossein Amirabdollahian said on Twitter. Tensions rose in Iran"s relations with the UAE after the U.S.-allied Gulf Arab state agreed last year to normalise ties with Tehran’s arch-foe Israel.