Oil prices rallied for a third-straight session on signs of higher demand and lower supply, including more bullish forecasts from both the Organization of the Petroleum Exporting Countries and the U.S. government.

OPEC’s new monthly oil-market report said demand for its crude will rise this year as the U.S. produces less and consumes more. It estimates that demand will grow to 29.2 million barrels a day, 100,000 more than a year ago. That reverses a forecast for a 300,000 barrel-a-day decline in demand. It also reduced non-OPEC...