Gary Gensler, chairman of the Securities and Exchange Commission, at the SEC headquarters in Washington, on July 22, 2021.Gary Gensler, chairman of the Securities and Exchange Commission, at the SEC headquarters in Washington, on July 22, 2021.

The SEC proposed two rule changes that would make it harder for US funds to make misleading claims about their environmental, social and corporate governance qualifications.

The proposals are subject to public feedback, which comes amid mounting concerns that some funds seeking to profit from the rise in ESG investing practices have misled shareholders over what's in their holdings.

The measures would give guidance on how to market the funds. The names rule would be updated to include characteristics related to ESG.

If a fund's name suggests it is focused on government bonds, at least 80% of its assets must be in that class. The change would make it possible for funds with certain characteristics to be included in the rules.

A lot has happened in our capital markets over the past two decades. SEC Chair Gary Gensler said in a statement that gaps in the current Names Rule may undermine investor protection.

Some funds claim that the rule does not apply to them, even though their name suggests that investments are selected based on specific criteria.

The amount of money put into global ESG funds increased to a record $649 billion in the year through November 30, up from $542 billion in 2020 and $285 billion in 2019. About 10% of worldwide fund assets are ESG funds.

In March, the SEC unveiled broad rules that would require publicly traded companies to disclose how climate change risks affect their business, as well as provide more information on how their operations affect the environment and carbon emissions.

ESG has a wide variety of investments and strategies. I think investors should be able to see what the strategies are all about.

Andrew Behar, president of the climate activist organization As You Sow, said that the new names rule won't stop misleading labeling for investors.

The new rule acknowledges the problem but doesn't fully address it. There is still a need for clarity on what sustainable is and other terms.

Rachel Curley, democracy advocate at the non-profit Public Citizen, said in a statement that the SEC's new rules on fund portfolios would begin to transform the landscape around investments.

Retail investors don't have a clear picture of what it means to invest in a sustainable fund.

After publication in the Federal Register, companies, investors and other market participants can comment on and suggest changes to the rules during a 60-day public comment period.

CNBC's Thomas Franck contributed to the report.