HOUSTON (Reuters) -Exxon Mobil Corp and a small activist hedge fund are waging a more than $65 million proxy fight over board seats, with the largest U.S. oil producer marshalling executives, TV appearances, social media and websites to rebut the challenge. The David-and-Goliath fight has Exxon determined to block Engine No. 1’s four nominees at its May 26 shareholder meeting, while urging shareholders reject proposals to split its chairman and chief executive roles, and block climate-related reports sought by other groups. Exxon has out-gunned its tiny rival’s $30 million budget with spending the company expects will be about $35 million above its usual proxy solicitation costs, according to regulatory filings. Some proxy experts said Exxon’s spending could reach $100 million, a figure the company rejects. Its campaign includes more than 130 proxy-related filings through April 14, about four times as many as its rival, a website, Twitter posts, blogs, and employee forums. “Don’t be deceived by a months’ old hedge fund, Engine No. 1, that wants your Company to pursue a vague and undefined plan – which we believe will jeopardize our future and your dividend,” Exxon wrote to shareholders this week. Investor Engine No. 1 last year took on the largest U.S. oil producer for “significant underperformance” and criticizing its lagging approach to cleaner fuels. Exxon’s historic $22.4 billion loss last year, three debt downgrades in two years and continued reliance on fossil fuels for future results has led to “the staggering decline of a once-iconic American company,” the hedge fund said. It asked shareholders to “review the facts and decide for yourselves,” in a letter this month. “Exxon Mobil’s scaremongering and efforts to obfuscate the facts are beneath it and we welcome a substantive debate as to the directors best suited to position the company for long-term success in a changing industry and world,” the fund said in a statement. Exxon has sought to blunt the fund’s nominees by expanding its board and adding director Jeff Ubben, who ran a sustainable investing fund. It also has pledged to increase low-carbon initiatives and lower the intensity of its oilfield greenhouse gas emissions. “Exxon Mobil will continue to provide updates on our strategy and plans to grow earnings and cash flow, pay and grow the dividend, fund high-value projects and position the company to have a meaningful role in the energy transition,” said Exxon spokesman Casey Norton. Slideshow ( 3 images ) ‘KICK IN THE PANTS’ Engine No. 1 and Exxon have been holding meetings and calls with institutional investors to press their cases, according to people familiar with the matter. Engine No. 1 has pressed the credentials of its board candidates, which include the former executive vice chairman of Marathon Petroleum Corp and the renewable fuels chief at Finnish refiner Neste Oyj. The fund has won support from California State Teachers’ Retirement System (CalSTRS), the second largest U.S. pension fund. Hedge fund D.E. Shaw plans to vote with the company, according to people familiar with the matter. But several other Exxon holders declined to say how they plan to vote. “Do I think that Exxon getting a kick in the pants is a bad thing? Absolutely not,” said Mark Stoeckle, senior portfolio manager at shareholder Adams Funds, which holds 1.45 million Exxon shares. As poorly as the company has performed, Stoeckle says replacing a large percentage of Exxon’s board seems an “overreach.” Given Exxon’s 2.8 million shareholders and 45% of its stock in the hands of individual holders, the battle could become one of the biggest proxy fights in history, said an executive at a proxy solicitation firm familiar with the matter. Exxon will pay $2.5 million plus expenses for solicitation firms Mackenzie Partners and D.F. King. The two have agreed to assign about 350 employees to the campaign, Exxon said. Activists typically have a hard time attracting shareholders to their battles, said Wei Jiang, who studies hedge fund activism as a finance professor at Columbia Business School. CalSTRS and Engine No. 1 is an “uncommon” alliance between a traditional investor and activist fund, she said. A big unknown is what top proxy advisors’ Institutional Shareholder Services Inc and Glass Lewis & Co will recommend. Both could release recommendations on the board seats, in mid-May, about two weeks ahead of Exxon’s shareholder meeting.