BAGHDADBAGHDAD (Reuters) - Saudi Oil Minister Khalid al-Falih made a high profile visit to Iraq on Saturday, calling for increased economic cooperation and praising existing coordination to boost crude oil prices.

In a speech at the opening of the Baghdad International Exhibition, Falih said cooperation between Iraq and Saudi Arabia contributed to "the improvement and stability we are seeing in the oil market"

Falih is the first Saudi official to make a public speech in Baghdad for decades. The two countries began taking steps towards detente in 2015 after 25 years of troubled relations starting with the Iraqi invasion of Kuwait in 1990.

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Tension remained high after the 2003 U.S.-led invasion of Iraq, which toppled Saddam Hussein. The American occupation of Iraq empowered political parties representing Iraq's Shi'ite majority, close to Saudi Arabia's regional rival Iran.

With a thaw in relations, Falih said a joint committee is "working on measures to speed up the establishment of an economic partnership and to reactivate cooperation and economic complementarity."

Iraq is seeking economic benefits from closer ties with Riyadh while Saudi Arabia hopes a stronger relationship with Baghdad would help rollback Iran's influence in the region.

Iraq lies on the fault line between Shi'ite Muslim power Iran and the Sunni-ruled countries that are its regional arch-rivals, chief among them Saudi Arabia.

Iraqi Prime Minister Haider al-Abadi left Baghdad on Saturday for a visit to Saudi Arabia, his second to the kingdom this year, his office said in a statement.

His talks with Saudi officials will focus on efforts to rebuild Iraq after the war on Islamic State and fostering economic and trade cooperation, the statement said. Abadi will visit other Middle Eastern countries after the kingdom, it said.

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"The best example of the importance of cooperation between our two countries is the improvement and stability trend seen in the oil market," said Falih, to applause from the audience of Iraqi ministers, senior officials and businessmen.

Saudi Arabia and Iraq are respectively the biggest and second biggest producers of the Organization of the Petroleum Exporting Countries (OPEC).

The Iraqi oil ministry said Falih and his Iraqi counterpart, Jabar al-Luaibi, would cooperate in implementing decisions by oil exporting countries to curb global supply in order to lift crude prices.

OPEC, Russia and several other producers agreed a pact at the start of 2017 to cut production in order to boost oil prices. The cutbacks should continue until March 2018.

Falih called for increased economic cooperation between the two countries at all levels, saying Saudi Arabia is implementing measures to facilitate the flow of goods and services between the neighbors.

A Saudi commercial airplane, operated by Flynas, arrived in Baghdad on Wednesday for the first time in 27 years.

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In August, the two countries said they planned to open the Arar land border crossing for trade for the first time since 1990.