Crude oil prices extended their rally beyond $50 per barrel Tuesday as demand pressures build up against supply outages, though underlying pessimism endures.

Consumer demand for petroleum products in the United States, the world's largest economy in terms of nominal gross domestic product, is on the rise as warmer summer weather encourages more travel. Supply outages in Canada and Nigeria, two of the largest exporters to the U.S. economy, are putting pressure on the U.S. market, however.

In a policy address Monday afternoon, U.S. Federal Reserve Chair Janet Yellen said many of the concerns about the low price of oil in early 2016 are in the rear-view mirror as many of the spillover effects of a weak energy market improve.

"New drilling and energy-sector employment have plunged, and the effects have spilled over to businesses serving the energy production sector," she said. "But the largest declines in drilling activity are likely now behind us."

A dismal jobs report from last week pushed major stock indices, as well as crude oil prices, lower. Yellen, however, said factors ranging from a steady value for the U.S. dollar and household spending meant the rate of inflation was moving closer to the 2 percent level desired by policymakers.

"The positive economic forces have outweighed the negative," she said.

Oil rallied strongly after Yellen's address and that momentum continued into early Tuesday trading. The price for Brent crude oil gained 0.7 percent to start the day at $50.90 per barrel. West Texas Intermediate, the U.S. benchmark price for oil, was up 0.6 percent to $49.99 per barrel in New York.

Looking ahead to a data release later this week from the U.S. Energy Information Administration, S&P Global Platts Oil Futures Editor Geoffrey Craig said market indicators should point to growing demand as the increase in refinery activity pulls domestic crude oil inventories lower.

A market that favored the supply side helped with the steady decline in crude oil prices for much of last year. If its forecasts are accurate and refinery utilization rates are on the rise, Craig suggested there may by some short-term durability in the rally.

"Another weekly decline in utilization -- which would be the third in a row -- would confirm the view that a seasonal drawdown [in inventories] is underway," he said in an emailed statement.

Recovery in crude oil prices, however, may encourage some drillers that were sidelined during the down turn to return to work. Data last week published by Baker Hughes show the long decline in rig activity in the United States was reversing. Meanwhile, S&P Global Platts said the 535.7 million barrels of oil in storage for the week ending May 27 is a 32.8 percent surplus to the five-year average for that time of year, suggesting some supply-side pressures remain.