* Putin discussed OPEC+ with MbS

* Putin discussed situation in Middle East

* MbS and Putin talked for three hours

* MbS says working on many issues with Russia

MOSCOW, Dec 7 (Reuters) - Russian President Vladimir Putin discussed OPEC+ cooperation on oil markets and the Middle East situation, the Kremlin said, during three hours of surprise talks with Saudi Crown Prince Mohammed bin Salman on Wednesday.

Mystery still surrounds the Kremlin chief's hastily arranged trip to Riyadh and Abu Dhabi, on which he was escorted by four Russian fighter jets, and it was not immediately clear what issue was so important for Putin to make a rare overseas trip.

Putin's meeting with the Saudi crown prince, who is known as MbS, came after oil prices fell despite a pledge by OPEC+, which groups the Organization of the Petroleum Exporting Countries (OPEC) and allies led by Russia, to further cut output.

MbS was shown greeting Putin with smiles and a effusive handshake as he emerged from his car in the Saudi capital.

"We talked again about cooperation in OPEC+," Kremlin spokesman Dmitry Peskov was quoted as saying by Russian news agencies.

"The parties agree that our countries bear a great responsibility for interaction in order to maintain the international energy market at the proper level, in a stable, predictable state," Peskov said.

Saudi Arabia and Russia are the world's two largest oil exporters, together controlling a fifth of the oil pumped each day.

MbS praised joint coordination between the two countries "that helped remove tensions in Middle East," Saudi state news agency SPA said.

"We share many interests and many issues that we are working on together for the benefit of Russia, the Kingdom of Saudi Arabia, the Middle East and the world as well," the agency quoted the crown prince as saying.

Russia's defence ministry had shown the Putin's Ilyushin-96 aircraft flanked by Sukhoi-35S fighter jets on its flight from Russia to the United Arab Emirates, his first stop on the trip.

MOSCOW OR RIYADH?

In Abu Dhabi, Putin said he intended to update President Sheikh Mohammed Bin Zayed Al Nahyan on the situation in the Ukraine.

A UAE official told Reuters that Putin's visit had allowed for an exchange of views on "a number of regional and international developments".

"The UAE is committed to continuous efforts with its international partners in working to reduce escalation, to find prospects for a peaceful political solution," the official said.

At the talks with MbS, Putin said that a planned visit by the prince to Russia had been changed at the last minute, prompting him to visit Riyadh.

"We awaited you in Moscow," Putin told MbS with a smile.

"I know that events forced a correction to those plans but as I have already said nothing can prevent the development of our friendly relations."

Putin then said: "But the next meeting should be in Moscow."

The crown prince said through a Russian translator that he was of course ready to do that.

"Then we are agreed," Putin said.

Putin's scope to travel abroad was limited in March when the International Criminal Court (ICC) issued an arrest warrant against him for the deportation of Ukrainian children to Russia.

Moscow denied the charge, which constitutes a war crime, and called the court's move outrageous, saying it was legally void in any case because Russia is not a member of the ICC.

Neither Saudi Arabia nor the UAE is a member of the court either, so Putin can travel to both without fear of being arrested under the ICC warrant. (Reporting by Reuters; Editing by Alexander Smith)