A day ago, Saudi Arabia depressed prices by saying it could raise its output by 25% if needed.
But prices rose again after the American Petroleum Institute said US supplies of crude oil fell last week, reversing a trend of rising supplies.
In afternoon trading in London, North Sea Brent crude was falling again, down 27 cents at $123.85 a barrel.
However, the benchmark contract in New York was up 56 cents at $106.17 a barrel. Crude oil prices have risen 25% since early September.
That is partly due to worries over Iran. It has threatened to disrupt supplies in the Gulf and there is also concern that its development of nuclear facilities could spark conflict in the region.
On Tuesday, Ali al-Naimi, Saudi Arabia's oil minister, said the country would step into the market if needed.
"My only mission is to convey to you that there is no supply shortage in the market," the minister said. "We are ready and willing to put more oil on the market."
Saudi Arabia is the world's biggest producer of crude oil, currently outputting 9.9 million barrels per day. The minister said it could boost output to 12.5 million barrels per day if needed.
Analysts say the latest news is pulling the oil market in different directions.
"The lower stocks are giving support to the market, but the Saudi comments will put a short-term cap on the oil price, and ease fears of supply issues emanating out of Iran," said Ben Le Brun, market analyst with OptionsXpress in Sydney.