Saudi Arabia is prepared to support extending oil cuts by OPEC and its allies into June and is also ready to prolong its own voluntary cuts to boost prices amid a new wave of coronavirus lockdowns, a source briefed on the matter said on Monday.

After steady oil price gains earlier this year, OPEC and its allies, known as OPEC+, had hoped to ease output cuts.

But a fresh wave of lockdowns to prevent a new surge in the virus has pushed oil off this year's highs, and four OPEC+ sources told Reuters this would most likely encourage the group to extend cuts into May when it meets on Thursday.

A Saudi oil source said on Tuesday OPEC+ had not taken any decision yet and discussions about policy had yet to start.

The source briefed on the matter said on Monday that Saudi Arabia was keen to extend cuts beyond May and into June.

"They don't see demand as yet strong enough and want to prevent prices from falling," the source said.

Under existing curbs, OPEC, led by Saudi Arabia, and non-OPEC producers, led by Russia, have cut just over 7 million barrels per day (bpd), while Saudi Arabia has made an additional voluntary reduction of 1 million bpd.

Last year, the group agreed to cut 9.7 million bpd, or about 10% of world output, but then eased back as demand recovered.

At a meeting on March 4, OPEC+ surprised the market by deciding to hold output broadly steady, although Russia and Kazakhstan were allowed slight increases.

A source familiar with Russia's thinking said on Monday Moscow would support extending cuts again while seeking another small rise in production for itself.

Benchmark Brent crude, which climbed above $71 a barrel shortly after the OPEC+ decision, reaching its highest since the pandemic began, is now trading around $65.

Alongside concerns about the pandemic's impact on demand, a rise in Iranian oil exports is also prompting caution. Iran has recently boosted shipments despite U.S. sanctions.

At a technical committee meeting on Tuesday, OPEC Secretary-General Mohammad Barkindo "emphasized the need to remain very cautious and attentive to changing market conditions," OPEC said.