NEW YORK — A federal agency tasked with looking out for consumers moved Monday to broadly ban the use of mandatory arbitration clauses, setting up a likely showdown with Republicans who oppose the change and want more control over the bureau in general.

The ban would apply when groups of customers want to file a class-action lawsuit against a bank or other financial company.

Mandatory arbitration clauses are found in the fine print of tens of millions of financial products, from credit cards to checking accounts. They require customers to use a private third-party mediator when they have a dispute, often giving up their right to sue a bank in court.

Because consumers generally don’t carefully read the fine print on the agreements for their checking accounts and credit cards, they are often unaware they are subject to arbitration. Even Wells Fargo banned customers from filing class-action lawsuits against it during the height of its sales practices problems, until pressure from politicians and outside groups led Wells to waive that right earlier this year.

Consumer advocates have been pushing for years for stricter federal regulation of these types of clauses. The clauses, said Richard Cordray, director of the Consumer Financial Protection Bureau, are a way for banks and other financial companies to “sidestep the legal system.”

The CFPB’s rules are not a total ban on arbitration clauses. Financial companies will still be able to force individuals to settle disputes through arbitration, but those kinds of cases are far less common. The ban also won’t apply to any existing contracts. So if a customer has a credit card with American Express, for example, that arbitration clause remains in effect. However if the person were to open a new credit card account with American Express after this rule went into effect, it would apply.

But the move by the CFPB — a high-profile independent agency created under President Obama — is likely to face pushback from the banking industry and the Republican-controlled Congress.

Congressional Republicans have been using a ’90s-era law known as the Congressional Review Act to roll back regulations issued in the final months of Obama’s administration. The law allows Congress, with a simple majority vote, to override an agency’s recently issued rules within 60 legislative days of it being finalized.

Cordray acknowledged that this rule is likely to face scrutiny from Congress. However, Congress has passed laws that ban arbitration clauses outright in other forms of financial products, notably mortgages and loans to servicemen and women.

“I am, of course, aware of those parties who have indicated they will seek to have the Congress nullify this new rule,” Cordray said in prepared remarks. “My obligation as the director of the Consumer Bureau is to act for the protection of consumers and in the public interest. In deciding to issue this rule, that is what I believe I have done.”

Republicans have also challenged the structure of the CFPB, believing Cordray has too much power to act on his own.