Crude oil prices recovered somewhat Wednesday on expectations of declining inventories, though uncertainty could upend the rally ahead of the Brexit vote.

Global stock markets were relatively muted Tuesday as U.S. Federal Reserve Chairwoman Janet Yellen told lawmakers that factors like China's stagnation and concerns about slow productivity growth were creating "headwinds" for future U.S. economic growth.

Crude oil prices opened lower Tuesday, but recovered somewhat after Yellen's comments. Downward pressure eased after a militant group in Nigeria, a member of the Organization of Petroleum Exporting Countries and one of the top oil exporters to the United States, denied it brokered a 30-day truce with the government.

Crude oil prices opened marginally stronger in early Wednesday trading. The price for Brent crude oil was up 0.7 percent to start the day at $50.97 per barrel. West Texas Intermediate, the U.S. benchmark price, gained 0.6 percent at the open to trade at $50.16 per barrel by the opening bell in New York.

A British referendum on membership in the European Union is set for Thursday. Economists have been warning of the economic fallout if the so-called Brexit strategy unfolds. In her prepared remarks, Yellen said a vote to exit the EU "could have significant economic repercussions."

Speaking to the BBC's Radio 4 on Wednesday, British Prime Minister David Cameron said a vote to leave would be the "wrong thing to do."

On the market front, data from the American Petroleum Institute released late Tuesday show domestic crude oil stockpiles declined 5.2 million barrels during the week ending June 17, a sign that demand is greater than supplies. Strains on domestic supplies may be in part reflected by the return of Canada to full production following last month's wildfires in Alberta and by ongoing militant activity in Nigeria.