Oil prices fell slightly on Tuesday as U.S. consumer confidence data weighed on markets and the government revised downward U.S. demand for July.

U.S. consumer confidence fell unexpectedly in September as the worst job prospects in 26 years fueled worries over personal finances, according to an industry report.

Oil markets have looked to wider economic data and equities markets for signs of a turnaround in the economy that could lift slumping fuel demand.

U.S. stocks <.N> traded lower after firming earlier on data showing U.S. single-family home prices rose in July from the previous month. The dollar rebounded from an eight-month low against the yen.

U.S. crude futures settled down 13 cents at $66.71 a barrel. London Brent crude futures fell 5 cents to $65.49 a barrel.

It seems pretty apparent that the market is tracking equities once again, said Gene McGillian, an analyst at Tradition Energy in Stamford, Connecticut.

Earlier today the market opened weak. Once the home index came out, the market turned around and seemed to gain some confidence that maybe some of the economic conditions are improving. That quickly dissipated after consumer confidence was reported to have fallen.

Further pressure came after the U.S. Energy Information Administration revised downward its estimate for July U.S. oil demand by 133,000 barrels per day to 4 percent below year-ago levels, marking the lowest July level in 13 years.

U.S. retail gasoline demand rose 0.9 percent last week compared with the previous week, however, according to a MasterCard SpendingPulse report.

Slowing demand in the United States and other developed economies knocked crude off record highs near $150 a barrel in July 2008 to below $33 a barrel in December. Crude has since found support on expectations of an economic rebound.

Traders were also keeping an eye on tensions between the West and OPEC member Iran over Tehran's nuclear program.

Iran said it would refuse to discuss a newly declared nuclear plant at forthcoming international talks and cautioned Western powers it could curb cooperation further if they repeated past mistakes.

Washington has suggested possible new sanctions on Iran's banking and oil and gas industries if Tehran fails to assuage Western fears it seeks nuclear weapons.

U.S. officials believe sanctions could now have more effect, playing on leadership divisions evident since a disputed presidential election in Iran.

The oil market was also awaiting weekly U.S. inventory reports, with analysts forecasting a 600,000-barrel build in crude stocks for the week to September 25, while gasoline and distillate inventories were also seen higher.

The American Petroleum Institute's report will be released late on Tuesday, with the EIA's report due out on Wednesday.

(Reporting by Matthew Robinson, Gene Ramos, and Robert Gibbons in New York; Ikuko Kurahone in London; Ramthan Hussain in Singapore; Editing by Walter Bagley)