Activist investors on Wednesday ousted two directors from ExxonMobil's board following criticism of its climate strategy.

The hedge fund Engine No. 1, which holds a 0.02% stake in Exxon, won two board seats in a vote during the company's annual shareholder meeting.

Engine No. 1 nominated four independent director candidates, receiving support from large pension funds such as CalPERS, calSTRS and New Yok State Common Retirement Fund.

As of Wednesday afternoon, two of the votes for the board seats were too close to call.

"We're looking forward to welcoming the new directors," Exxon CEO Darren Woods told CNBC. "I look forward to helping them understand our plans and then hear their insights and perspectives."

Engine No. 1 has targeted Exxon's board of directors since December as it has pushed for the company to consider how its role might change in a carbon-free society.

"A refusal to accept that fossil fuel demand may decline in decades to come has led to a failure to take even initial steps towards evolution and to obfuscating rather than addressing long-term business risk," the firm said in its investor presentation.

On Monday, Exxon said it would add two new directors including "one with energy industry experience and one with climate experience" in the next 12 months, but Engine No. 1 said the pledge was not substantial enough.

"What the board needs are directors with experience in successful and profitable energy industry transformations who can help turn aspirations of addressing the risks of climate change into a long-term business plan, not talking points," the firm said Monday.

The victory for Engine No. 1 comes as Exxon has recovered from its pandemic lows with shares up more than 40% in 2021 as it has cut costs and oil prices have bounced back, leading the company to a profit in the first quarter of 2021 after four straight quarters of losses.

Also, the District Court in The Hague last week ordered Exxon competitor Shell to reduce its net carbon dioxide emissions by 45% compared to its 2019 levels.

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