The Saudi oil minister expects prices to rise to $75 this year
Oil prices jumped more than 3% on Monday to a nearly seven-month high above $68 a barrel.
US light sweet crude settled $2.27 higher at $68.58 while Brent crude rose by $2.45 to $67.97.
Gains in global stock markets and data showing modest growth in Chinese manufacturing appeared to be driving up prices, continuing a recent rally.
Oil prices climbed by 30% in May, which was the largest gain in a single month since 1999.
But oil is still trading well below the record high of $147 a barrel seen last July.
Some analysts fear that the oil market may be moving ahead of reality, and warn that prices could fall as investors face up to the reality of a glut of supplies and weak global demand.
"Most of the commodity markets, the base metals as well as oil, have moved to factor in economic recovery," said David Moore, commodity strategist at Commonwealth Bank of Australia.
"There is a risk that if economic data does not continue to support this view of the world that markets become disappointed with the pace of economic recovery, leading to price setbacks."
Last week, ministers from the Opec group of oil-producing countries said that they would keep output unchanged, with the Saudi oil minister Ali al-Naimi predicting prices will reach $75 this year.