Crude oil prices moved lower at the start of trading Tuesday as supply-side pressures endured, even after a U.S. crude oil pipeline returned to service.

Oil moved sharply lower in early Monday trading after Iraq, one of the main contributors to production from the Organization of Petroleum Exporting Countries, said it wanted to be excluded from a production arrangement proposed last month in Algeria.

Iraq accounted for about 10 percent of OPEC's total output last month. Total OPEC production is already near the high end of the level outlined in Algeria and further exemptions would make the agreement difficult to uphold.

The U.S. Energy Information Administration offers data Wednesday that will give traders an assessment on whether or not the market was continuing its migration toward a decent balance between supply and demand. A glut of oil on the market early this year pulled crude oil prices below $30 per barrel.

Analysis emailed from S&P Global Platts late Monday said it expected to see U.S. crude oil inventory levels increase by 400,000 barrels from the previous week. That estimate followed a brief outage of a crude oil pipeline from the main U.S. oil storage facility in Cushing, Okla. That pipeline returned to service Monday evening.

Crude oil prices lost ground for the second straight session on Tuesday. The price for Brent crude oil was down 0.8 percent to open the day at $51.06 per barrel. West Texas Intermediate, the U.S. benchmark price for oil, was down 0.6 percent to start off the day at $50.23 per barrel.

WTI dropped briefly below $50 per barrel during trading Monday.

Oil priced at around $50 per barrel has brought with it confidence about a recovery in the energy market. Oilfield services companies Baker Hughes and Schlumberger both expressed sentiment that a rebound was on its way, particularly for North America.

Geoffrey Craig, a futures editor for Platts, said that, with exploration and production activity on the rise, supply-side pressures could be building along with higher crude oil prices.

"One wild card moving forward could be U.S. crude oil production, which estimates show has bottomed and could be headed higher given the uptick in drilling and hedging activity," he said.