Anti-corruption advocates are mounting opposition to a proposed rule by the Securities and Exchange Commission that would shield oil, gas and mining companies from investor lawsuits if they make false or misleading statements about payments to foreign governments.

The rule, part of a 102-page proposalpublished last month, would allow energy companies listed on U.S. stock exchanges to "furnish" rather than "file" payment information about their projects in foreign countries, a subtle shift that would reduce legal liability,...