The price of oil in New York is back below $40 a barrel for the first time in more than two weeks.
The Saudi plan to raise output still lacks Opec's full support
The 3.1% fall to $39.44 a barrel followed comments by Opec that it was considering an output boost big enough to make a "psychological impact".
Saudi Arabia, the world's biggest oil producer, has already announced it will unilaterally pump 10% more oil.
Ministers from the 11-member oil cartel are to meet in Beirut next week to discuss a broader rise in production.
In London, the price of Brent crude dropped 83 cents to $36.25 a barrel.
Supply and demand
Prices have been soaring throughout May thanks to the combination of strong demand, particularly from the US and the booming Chinese economy, and ongoing security fears.
The price of crude in New York topped $40 a barrel on 11 May, and has been close to 21-year highs ever since.
In the US, the effect has been to push petrol prices well beyond $2 a gallon, sky-high by American standards.
Even Saudi Arabia's offer made little initial difference, since the rest of Opec, supplier of a third of the world's oil, is breaking quotas and is believed to have little immediate headroom.
Opec president Pernomo Yusgiantoro said on Thursday that the cartel probably needs to boost production by more than the 2.3 million barrels a day Saudi Arabia suggested if the increase is to have much effect.
The option of going above that, he said, would be "a significant increase so as to give a psychological impact to reducing oil prices".
Even ahead of the Opec meeting, Saudi Arabia is now considering a long-term rise in capacity beyond the current 10.5 million barrels a day.