(Adds detail) April 23 (Reuters) - New York state’s pension fund on Friday threw its support behind an activist fund’s slate of nominees to Exxon Mobil Corp’s board, heating up a proxy fight for the company’s future. The biggest U.S. oil producer Exxon and activist hedge fund Engine No. 1 are battling over board seats following Exxon’s historic net annual loss of $22.4 billion for 2020. The fund has criticized the producer for “significant underperformance” and a lagging approach to cleaner fuels. The Exxon board “needs an overhaul,” to better manage climate risks and guide the company to a low carbon future, said N.Y. State Comptroller Thomas DiNapoli. Engine No. 1’s four director nominees “bring transformative industry experience,” he said. 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. New York state pension funds overseen by DiNapoli will vote in favor of Exxon board members Ken Frazer and Ursula Burns, but will withhold votes on the remaining five directors, it said. The funds hold 8.14 million shares of Exxon, according to Refinitiv. The fund has previously led shareholder proposals calling on Exxon to detail on its business could be affected by climate change. It also has supported proposals to split the CEO and chairman’s roles at the oil producer. (Reporting by Jennifer Hiller and Gary McWilliams Editing by Marguerita Choy)