By Ross Kerber and Svea Herbst-Bayliss

NEW YORK (Reuters) -Exxon CEO Darren Woods on Tuesday had warning words for activist shareholders thinking to emulate those who filed a climate-related shareholder proposal at the largest U.S. oil company.

Exxon sued the investors early this year and Woods indicated the company was ready to repeat the exercise against others he said might "abuse" the proxy proposal process.

“We hope we don’t have to use that action in the future. But if we find people continue to abuse the process, we’re going to hold them to the rules," Woods said.

Woods spoke via video link to a meeting of the Council of Institutional Investors in New York, which represents pension funds and other institutional investors.

Exxon had sued activists Follow This and Arjuna Capital in January after they filed a climate-related resolution for the company's annual meeting in May. A judge ultimately dismissed the suit in June, but only after the defendants withdrew their resolution and promised not to resubmit a similar one or help others do so.

The suit raised concerns it would diminish shareholders' influence. Woods said there is a still wide door for investors to make suggestions to companies.

But the proxy system, while well-intended, can be abused under regulators' current guidance, said Woods. He said established protocols, including using the courts, must be followed.

"We are not opposed to the shareholder proposal process," Woods said, but added that "We will insist it is used appropriately."

Woods faced skeptics in the audience including fund managers who, because of the lawsuit, had voted against Woods and other Exxon directors at the company's annual meeting in May. Nonetheless, Woods and other Exxon directors cruised to re-election with backing from big investors BlackRock and Vanguard, recent filings showed.

Some of the critical votes came from the California Public Employees' Retirement System, the largest U.S. pension fund. Its CEO Marcie Frost said via e-mail after the event that "We hope the issue is settled. CalPERS believes all shareholders have the right to be heard, whether they agree or disagree with the actions of a company’s leaders."

Sanford Lewis, an attorney who has represented Arjuna and other shareholder activists, said Exxon's suit could have a lasting effect on future proxy seasons.

"Small shareholders are going to think twice" about whether to file resolutions, Lewis said at the event, after Woods finished speaking.