But an early rally on Wall Street petered out after the yield on the 10-year U.S. Treasury bond jumped, amplifying worries over an inflation spike that potentially could lead to a shift in monetary policy.
The broad-based S&P 500 slipped 0.1 percent, while the Dow Jones Industrial Average gained the same amount in the first trading session after a holiday weekend.
London, Frankfurt and Paris posted solid gains.
The 23-nation OPEC+ alliance agreed after a very brief meeting to continue boosting production through July, leaving open the question of what they will do in August and beyond.
Oil prices hit a two-year peak during the session and petroleum-linked shares gained ground, boosted by the accelerating economic reopening and increase in travel demand, which raises orders for fuel.
West Texas Intermediate crude hit $68.87 a barrel in afternoon trading, while Brent North Sea reached for $71.34, before easing back.