Light sweet crude-oil futures fell 26 cents to stand at $66.58 a barrel in electronic trading.
Even though crude rose on Monday, analysts pointed out that the futures contract didn't climb as much as stocks did, indicating that what's been a close correlation between stocks and oil may be breaking down.
"The price action was capped given that a rally in the equity market found itself at odds with a newly discovered strength in the U.S. dollar," said analysts for ODL Securities in London.
"Technically, crude prices are now some way below the moving averages although its next direction is likely to remain a function of developments in the currency and stock market," they added.
Meanwhile, traders were positioning themselves ahead of a pair of weekly updates on U.S. inventories, from the the American Petroleum Institute and the Energy Information Administration.
Analysts foresee an increase of 2.1 million barrels for the week ended Sept. 25 as refinery throughputs are expected to drop, according to a Platts survey of analysts.
Elsewhere, the ICE-traded Brent contract fell 43 cents to $65.11 a barrel
