Calpers, the biggest public pension plan in the United States, is considering a vote against ExxonMobil chief executive Darren Woods’ re-election to the company's board in the face of shareholder discontent over a lawsuit it filed against two climate-focused investors, the Financial Times reported on Friday.

Investors led by U.S. activist investment firm Arjuna Capital and shareholder activist group Follow This earlier this year asked Exxon and other oil majors to adopt tighter climate targets and to set targets to reduce emissions produced by users of its products.

In January, Exxon filed a complaint in a Texas court seeking to prevent a climate proposal by activist investors from going to a vote during the company's shareholder meeting in May.

Arjuna Capital and Follow This subsequently withdrew the proposal but Exxon said in February that it would continue to pursue a lawsuit against the two activist investors.

California Public Employees' Retirement System (CalPERS)chief operating investment officer Michael Cohen told the newspaper that the pension fund was "deeply concerned" about the case, adding it appeared to be an effort to silence critical shareholders.

"Exxon has gone well beyond any other company that we’re aware of in terms of suing shareholders for trying to bring forward a proposal," he told the newspaper. The fund holds 0.2 percent equity stake in Exxon, based on recent regulatory filings.

Calpers did not immediately respond to Reuters request for comment. Exxon could not be immediately reached for a comment.

When asked if Calpers is considering voting against Woods’ re-election as board chair Michael Cohen, Calpers' operations chief said "correct", adding that "there were conversation happening right now.

(Reporting by Kanjyik Ghosh and Dagmarah Mackos; Editing by Nivedita Bhattacharjee)