Reuters - Russian President Vladimir Putin and Saudi Crown Prince Mohammed bin Salman spoke by phone on Thursday and underlined the importance of further cooperation within the OPEC+ group of oil producers, the Kremlin said.

The conversation took place six days after U.S. President Joe Biden visited the prince in Saudi Arabia - highlighting the kingdom's importance to both Washington and Moscow at a time when Russia's war in Ukraine is roiling global energy markets.

On June 2, OPEC+, which brings together the Organization of the Petroleum Exporting Countries with other producers led by Russia, agreed a larger-than-expected rise in output, a step welcomed by Biden after the United States had called for more supply.

Sources told Reuters that Saudi Arabia consulted closely with Russia before pushing for the production hikes.

Riyadh wants to keep Russia on board to increase leverage in the oil market, while Moscow gains from being part of OPEC+ at a time when the West is trying to strangle its economy with sanctions over the war.

"The current situation on the world oil market was considered in detail. The importance of further coordination within the framework of OPEC+ was emphasized," the Kremlin said in a readout of the call.

"It was noted with satisfaction that the countries participating in this format are consistently fulfilling their obligations in order to maintain the necessary balance and stability in the global energy market."

Biden ended his Middle East trip last week without any announcement that the kingdom would raise oil production to bring down fuel prices, which are spurring the highest U.S. inflation in four decades.

Saudi Foreign Minister Prince Faisal bin Farhan Al Saud said oil was not discussed at a U.S.-Arab summit on Saturday, and OPEC+ would continue to assess market conditions and do what is necessary. The producer group is due to meet again on Aug. 3.