U.S. banks are seeking to limit the reach of the Volcker Rule by challenging its definition of what it means to own a hedge fund or private-equity fund.

The opening gambit was made by the American Bankers Association (ABA), the industry's biggest lobbying group, which said in a federal lawsuit filed last month on behalf of community banks that regulators had defined too broadly what it means to have an ownership stake. A week later, four other organizations, including the Financial Services Roundtable, sent a letter to bank-supervisory agencies making the same point.

Regulators, who spent more than two years writing the rule, defined ownership widely to capture all economic interests a firm might have in restricted funds. The ABA said it should be narrower, focusing only on equity, and that buying debt a fund sells doesn't qualify as ownership. If the industry succeeds in getting the definition narrowed, that could allow banks to have ties to funds the rule intended to outlaw.