Traders were also awaiting the Federal Reserve's latest decision on US interest rates also due today.
New York's main oil futures contract, light sweet crude for August delivery, dipped 13 cents to $136.87 per barrel.
Brent North Sea crude for August climbed by four cents to $136.50.
"Crude futures were almost unchanged ... With investors awaiting important data," said Sucden analyst Andrey Kryuchenkov.
The US Department of Energy was to publish its latest weekly US fuel stockpiles report, with analysts forecasting a drop in crude oil inventories.
"In addition to tight supplies, a weaker dollar could also be supportive to oil prices," said Kryuchenkov.
"Today (Wednesday), the US central bank is expected to leave interest rates unchanged at two percent amid disappointing data recently, which could put some pressure on the dollar and support crude futures."
A weaker dollar sparks demand for oil as it becomes cheaper for foreign buyers.
Oil prices have almost doubled over the past year after striking record highs of close to $140 a barrel last week.
Saudi Arabia, the world's largest exporter of crude oil, recently agreed to raise its daily output by more than 200,000 barrels to 9.7 million.
OPEC president Chakib Khelil and other oil producers are opposed to higher output, blaming rocketing prices on speculative buying by funds.
