The two companies were questioned by Republican attorneys general from 21 states earlier this month about whether their guidance on issues like climate change or boardroom diversity violate their duties to clients.

In a response letter dated Jan. 31, Glass Lewis Executive Chairman Kevin Cameron pushed back on the suggestion and said that under the firm's benchmark policy it routinely recommends against shareholder proposals "that — however worthwhile as a social goal — have not demonstrated a nexus to shareholder value."

In addition, Cameron wrote that issues like how companies manage the risks and opportunities presented by climate change "is widely recognized as a material risk-return factor today." Nearly all companies in the S&P 500 now publish sustainability reports using various third-party standards, he noted.

In a separate letter provided by a spokesman, ISS Chief Executive Gary Retelny wrote that while environmental, social and governance (ESG) considerations have grown more important to investors, "fulfilling our fiduciary and contractual responsibilities to our clients remains the foundation of our business."

The two leading proxy advisers provide suggestions on how clients like pension plans should vote on everything from electing board members to signing off on executive pay at corporate annual meetings.

In the past, both have faced criticism from corporate executives over advice for shareholders to vote against board recommendations. Last week Tesla Inc. Chief Executive Elon Musk said in a tweet that the two firms have "far too much power."

But academic reviews have found mixed evidence about the firms' impact as big shareholders like BlackRock Inc. and Vanguard Group, under pressure from socially minded investors, put more resources into determining their ESG-related votes.