The investor, Engine No. 1, is a small fund that last year took on the top U.S. oil producer for what it said was poor financial returns and a lagging approach to cleaner fuels. Exxon since has vowed to cut its debt, invest more in low-carbon initiatives, and improve returns.

The fund singled out for removal three former chief executives of prominent U.S. companies and the former head of Malaysia's state-run oil firm who joined the board last month. Its nominees for the board include a former U.S. Energy Department official and an executive at a wind turbine developer-manufacturer.

Exxon has named three new directors since February, including Wan Zulkiflee Wan Ariffin, the former CEO of Malaysia's Petronas.

Engine No. 1, which counts pension fund California State Teachers' Retirement System (CalSTRS),among its supporters, asked shareholders to vote against the re-election of former MetLife CEO Steven Kandarian, former Caterpillar CEO Douglas Oberhelman, former IBM CEO Samuel Palmisano, and Wan Zulkiflee.

The three U.S. executives "have destroyed shareholder value and generated significant long-term risk for investors," Engine No. 1 said in a statement. Wan Zulkiflee, who was appointed to Exxon's board last month after Engine No. 1 launched its campaign, "is not as relevant for a public company in need of transformative and successful energy experience," the fund said. A spokesperson declined comment beyond its statement.

"We categorically disagree with Engine No. 1's assertions about our board, including the directors they have targeted," said Exxon spokesman Casey Norton. A board committee considered Engine No. 1's candidates and ruled them out, his statement added.

Exxon directors "have experience leading some of the world's largest, most complex and successful companies and bring to the board a wide range of backgrounds, knowledge and skills relevant to the company's business and future direction - unlike the Engine No. 1 candidates."

The activist fund nominees include Gregory Goff and Anders Runevad, former chief executives of oil refiner Andeavor and wind-turbine manufacturer Vestas Wind Systems, respectively; Kaisa Hietala, former head of renewable fuels at Finish refiner Neste; and former U.S. Assistant Secretary of Energy for efficiency and renewable energy, Alexander Karsner.

(Reporting by Shariq Khan in Bengaluru and Gary McWilliams in Houston; Editing by Krishna Chandra Eluri, Bernadette Baum and David Gregorio)