The U.S. Consumer Financial Protection Bureau is calling on credit card companies to provide free credit scores to their customers, a move that would help tens of millions of people monitor their financial status.

The agency announced Thursday that Director Richard Cordray wrote to top card companies this month, strongly encouraging them to share credit scores and related information at no charge.

"Consumers often learn the importance of their credit standing when it is too late: after a credit application is denied or identity theft has occurred," Cordray said in the letter.

About 157 million Americans have one or more credit cards, according to TransUnion, meaning free credit scores would be widely available if card issuers adopt the policy widely.  About 200 million people have a credit file with TransUnion, Experian and Equifax, the big three credit reporting bureaus.

In November 2013, credit score supplier FICO announced that it would allow lenders to share copies of credit scores with their customers, at no extra cost. Discover, First Bankcard and Barclaycard have opted in to the program, providing individuals' FICO scores on periodic statements or via customer service websites.

Without mentioning the card issuers or FICO directly, Cordray referred to the recent moves by some banks to make free credit scores available. He called for scores and related educational information to be provided through existing communications, such as monthly statements.

Regular access to credit scores can alert people to identity theft, the CFPB said, as well as provide them with a picture of their creditworthiness. The FICO credit score is the main score used by lenders to evaluate applicants for home loans, auto loans and credit cards.

The announcement came as the watchdog agency announced a report that highlighted problems consumers have with credit reports.  Data on credit reports are the basis of FICO credit scores, which analyze consumers' available credit and their loan repayment history.

 The CFPB said its analysis of consumer complaints found widespread problems with inaccurate information and difficulties with correcting entries. Of 31,000 consumer complaints filed with the CFPB from Oct. 2, 2012 to Feb. 1, 2014, nearly three-quarters concerned inaccurate information, the agency said.  Eleven percent of complaints were dissatisfied with how the reporting bureau handled a dispute over an entry, and 9 percent of complaints had trouble obtaining a free annual credit report, their right under the Fair and Accurate Credit Transactions Act.

See related: Credit report complaints highlight errors, Discover expands free FICO credit score program