Brent turned slightly higher and U.S. oil settled lower, as the euro and dollar reacted to the European Central Bank's rate cut.
Crude pared gains, shrugging off some positive signals as traders took profits following strong gains on Monday.
The dollar extended gains against the euro, amid expectations that the Federal Reserve could raise rates sooner than expected.
Stocks extended a record climb on Friday after the May jobs report.
Asia stocks ended mostly higher on Tuesday following a pick up in Chinese consumer inflation, but Japanese shares fell on profit-taking.
U.S. stocks tallied slight gains on Monday, with benchmark indexes again closing at records.
Prices for Treasurys fell, pressured by sale of new coupon-bearing government debt this week and a greater risk appetite after a strong jobs report.
European shares started the week on a positive note, closing higher, as U.S. stocks advanced near record high territory.
Crude rose as strong Chinese and U.S. data pointed to healthy economic growth and higher demand for oil from the world's top two consumers.
U.S. stock index futures pointed to a lower start to Wall Street trade on Tuesday, despite more upbeat news out of China.
Gold held above $1,250 an ounce on Monday after U.S. jobs data matched expectations, while a rally in stocks curbed the metal's appeal.
Asian stocks kicked off the week with gains following positive data releases from the region's two biggest economies and a strong U.S. lead.
U.S. stock index futures pointed to a flat-to-lower open on Wall Street on Monday, despite upbeat data from China and Japan.
Treasury prices fell ahead of a $62 billion sale of new coupon-bearing government debt next week.
European shares continued their push higher to close up on Friday, after investors reacted positively to U.S. payrolls data.
Crude pared gains on Wednesday, amid news that Ukraine's president-elect was working on a peace plan with Russia.
The euro rose against the dollar and the yen on Monday, on confidence that the ECB will not be easing policy again soon.
Gold fell as the dollar swung into positive territory, after the U.S. jobs report came in almost exactly in line with expectations.
The euro weakened against the dollar, as yield differentials between Treasuries and Bunds widened to multi-year highs.
Asian shares were mostly lower on Friday as caution over U.S. jobs data overshadowed Wall Street's record and the ECB's stimulus measures.
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