Shareholders will be asked to vote on the pay of the company's executives at it annual general meeting in London on April 14.

BP, like its rivals, has faced a near 70 percent drop in oil prices since mid-2014, which has led to thousands of job losses and spending cuts in the industry.

"We have strong concerns regarding pay outcomes relative to financial performance and investor outcomes in respect of the past fiscal year," Glass Lewis said in a report.

"In particular, we note that bonus payouts to the executive directors were at 100 percent of maximum opportunity despite the lacklustre overall performance during fiscal year 2015."

"Given our concerns regarding bonus payouts and the overall incentive structure, we do not believe shareholders should support the remuneration report at this time."

BP said in response that Dudley's remuneration, which rose by 20 percent from a year earlier, "is primarily based on true underlying performance, not factors over which the executives have no control."

"BP executives performed strongly in a difficult environment in 2015, managing the things they could control and for which they were accountable," the company said in a statement.

"The annual cash bonus is based on measures directly linked to BP's strategy, and results were strong across all measures. Safety and operational risk performance was excellent and BP responded quickly and decisively to the drop in oil price.

Last year, more than 86 percent of shareholders voted in favour of Dudley's pay package.

(Reporting by Ron Bousso. Editing by Jane Merriman)

By Ron Bousso