As of July 1 (07:48, Moscow time), Brent Crude futures for September delivery rose by 0.16% to $74.74 a barrel.
Light Sweet Crude (WTI) futures for August delivery on the New York Mercantile Exchange rose by 0.2% to $73.62 a barrel..
Oil prices climbed in early Asian trade on Monday, underpinned by the bright outlook for fuel demand growth in the next quarter, while investors looked ahead to the OPEC+ meeting this week for supply guidance.
Brent crude futures for August nudged up 7 cents, or 0.1%, to $68.79 a barrel by 0038 GMT after settling at their highest in two years on Friday.
U.S. West Texas Intermediate crude for July was at $66.45 a barrel, up 13 cents, or 0.2%.
Separately, crude output in the United States soared 14.3% in March, the Energy Information Administration reported on Friday, while Baker Hughes data showed oil and gas rigs rising for a 10th month in a row last week.