MOSCOW, Oct 10 (Reuters) - Russian President Vladimir Putin hosted Iraqi Prime Minister Mohammed Shia Al-Sudani in the Kremlin on Tuesday and praised cooperation between their countries at the OPEC+ group of top oil producers, saying it had helped to stabilise energy markets.

"We coordinate work within the framework of OPEC+ and do this very successfully with the aim of stabilizing the situation on world markets. Overall, we succeed in this, and I hope we will continue to work with you in the future," Putin told Sudani at the start of their first ever meeting.

The Organization of the Petroleum Exporting Countries (OPEC), Russia and allied producers are known as OPEC+. Putin pays close attention to the oil and gas business, sales from which generate around a third of Russia's state budget proceeds.

Iraq is OPEC's second-largest oil producer after Saudi Arabia.

Saudi Arabia and Russia have agreed to continue with voluntary oil supply cuts of a combined 1.3 million barrels of oil per day, or more than 1% of global demand, to the year-end.

Putin's meeting with Sudani took place against the backdrop of the conflict between Israel and Palestinian militants in Gaza that has seen hundreds killed on both sides since the weekend.

Sudani underlined Iraq's continued support for the Palestinian cause and urged Russia to use its status as a permanent member of the U.N. Security Council to help halt Israel's strikes against the Palestinian Territories, according to a statement released by his office.

Earlier, Putin said the explosion of violence between Israel and the Palestinians showed the failure of U.S. policy in the Middle East. The Kremlin said it was in touch with both sides.

ENERGY COOPERATION

Sudani, who is on a two-day trip to Moscow, will meet Putin again on Wednesday when the two leaders participate in an energy forum, the Kremlin said.

The Iraqi statement on Tuesday's talks in the Kremlin said Sudani and Putin had focused on enhancing bilateral relations and joint cooperation, especially in the energy sector, including the activities of Russian oil companies in Iraq.

Putin said in a televised excerpt of their talks that Russia's investments in Iraq totalled around $19 billion.

Russia's biggest oil company Rosneft has been making deals with the Kurdistan Regional Government of Iraq since at least 2017, pumping billions of dollars there in oil producing and shipping infrastructure.

Russia's Lukoil now produces some 480,000 barrels per day of oil at Iraq's southern West Qurna 2 oilfield, while Russia's Gazprom Neft, the oil arm of the gas giant Gazprom, is involved in the Badra oil field project in eastern Iraq and two fields in Iraqi Kurdistan. (Reporting by Lidia Kelly in Melbourne, Vladimir Soldatkin in Moscow and Timour Azhari in Baghdad; Editing by Michael Perry and Gareth Jones)