WASHINGTON — Banks could invest heavily in or even sponsor venture capital funds under a proposed change to a post-crisis rule that was intended to limit their risk-taking.

The proposal, unveiled Thursday by the Federal Reserve and other banking agencies, would revamp the Volcker Rule, which was created as part of the 2010 Dodd-Frank law. The rule restricts banks like Goldman Sachs and J.P. Morgan from making risky bets with customer deposits and generally prevents firms from sponsoring or investing in private equity and hedge funds.

The proposed changes would loosen some of those restrictions, allowing banks to invest in some credit funds and either sponsor or take ownership stakes in venture capital funds, which pool ultrarich investors’ money and make high-risk investments in start-ups that can yield enormous returns or huge losses.

Restrictions would apply: Banks could not guarantee the funds’ performance, for instance.

Regulators portrayed the changes as common-sense adjustments that will allow banks to better support small businesses by providing capital. Fed Chair Jerome H. Powell said the changes would “permit banks to provide limited services to covered funds in ways that do not raise the types of concerns the Volcker rule was intended to address.”