Saudi Aramco notified its customers in North Asia on Wednesday that they will receive the entire volumes of crude oil that they requested in June, several sources with knowledge of the matter told Reuters.
But some Chinese refiners have requested lower supply volumes in June, said the sources.
It is not known how much less crude the Chinese refiners asked for in June. Two sources estimated it could be up to 5 million barrels less than May.
Aramco lowered its official selling prices for all crude grades to buyers from Asia for June-loading cargoes amid lower refining margins. However, the cut was less than what the market expected.
The falling profit margins have prompted refiners to seek cheaper oil from other suppliers, such as Russia, or even consider lowering operational rates.
China is stepping up to increase its purchases of low-priced Russian oil and raise its share of the Urals oil market, dominated by Indian refiners.
The overall supply volumes come even as the Organization of the Petroleum Exporting Countries (OPEC) and allies, known as OPEC+, announced output cuts of 1.16 million barrels per day (bpd) starting from May for the rest of the year.
Saudi Arabia, the world's top oil exporter, will reduce production by 500,000 bpd under the cuts.
Meanwhile, oil prices fell in trading on Wednesday after sector data showed a sudden increase in US crude inventories, while investors expected the US consumer price index for April to show high inflation.
Brent crude fell 60 cents to $76.84 a barrel, and US West Texas Intermediate crude fell 68 cents to $73.03.
In a possible sign of weak demand, US crude oil inventories rose by about 3.6 million barrels in the week ending May 5, while gasoline stocks rose by 399,000 barrels, the American Petroleum Institute (API) reported.
Separately, the Russian news agency Tass said the Russian oil pipeline operator Transneft confirmed reports about an attempt to carry out a terrorist act on the Druzhba pipeline system.
Transneft reported that no one was injured in the incident.
Meanwhile, British Prime Minister Rishi Sunak said the UK would need fossil fuels in the "next few decades" as the UK moves to eliminate greenhouse gas emissions after it was urged to oppose the private Rosbank oil field project in the North Sea.
"It makes absolutely no sense to not invest in the resources we have here at home, to import foreign fossil fuels, not create jobs here and import them at twice the carbon emissions as our local resources," Sunak told lawmakers in weekly questions in the House of Commons on Wednesday.
"It is an economically illiterate policy."