WASHINGTON >> American Express Co. is paying $112.5 million in refunds and fines to settle regulators’ accusations that it charged unlawful late fees and deceived customers to pressure them to pay off old debts or buy extra credit card services.

The company agreed to the settlements announced today by four federal agencies, including the Federal Reserve and the Consumer Financial Protection Bureau, and Utah regulators.

American Express is refunding $85 million to about 250,000 customers and is paying $27.5 million in civil fines.

The agencies said American Express violated federal laws prohibiting deceptive practices by using false statements to get customers to settle old debts. The regulators say that included falsely telling customers that if they agreed to settlements to partially pay off their debts, the remaining balance would be forgiven.

The violations were said to have occurred from 2003 to this past spring.

The director of the Consumer Financial Protection Bureau, Richard Cordray, said in a statement that the company violated consumer-protection laws “at all stages of the game — from the moment a consumer shopped for a card to the moment the consumer got a phone call about long overdue debt.”

American Express also charged late fees on some credit cards based on a percentage of the debt owed, a violation of a 2009 law prohibiting certain credit card practices, the regulators said.

They said customers were sometimes led to believe they would get $300 as well as bonus points if they signed up for Amex’s “Blue Sky” credit card program. Customers who met the conditions didn’t receive the promised $300, according to the agencies.

In addition, they said the company:

—Unlawfully discriminated against consumers applying for new card accounts on the basis of age.

—Failed to report customer disputes over billing to the consumer-credit reporting agencies.

New York-based American Express also agreed to end the practices and to hire independent auditors to ensure the company’s compliance with consumer-protection laws.

The company said most of the $85 million in refunds is related to late fees and debt collection practices. Customers entitled to refunds will be notified as soon as possible, it said.

Amex also said in a statement that it has put together plans to correct each of the violations cited by the regulators. “The company is strengthening its internal compliance processes and will continue to work closely with its regulators,” the statement said.

Amex also noted that it has previously set aside reserves to cover a large part of the refunds and fines.

Unlike Visa and MasterCard, which only process transactions, Amex issues its own credit cards. When customers charge more on their Amex cards, the company earns even more in interest income and a variety of fees. Amex calls itself the world’s largest credit card issuer by volume of customer purchases.

Also reaching settlements with the company were the Federal Deposit Insurance Corp. and the U.S. Office of the Comptroller of the Currency, a Treasury Department agency that regulates national banks.

Federal regulators are examining the sale of add-on credit card products in the financial industry overall.

The alleged violations by Amex were discovered during a routine examination of the company’s bank subsidiary by the FDIC and the Utah banking agency, the regulators said Monday. Parts of the investigation then were transferred to the Consumer Financial Protection Bureau.

That agency, which began operations last year, was created by the 2010 financial overhaul law to protect consumers from excessive or hidden fees and other financial threats. Its settlement with Amex is its fourth public enforcement action. Last week, the consumer bureau and the FDIC announced an agreement by Discover Bank to refund $200 million to customers and pay $14 million in fines to resolve accusations that it pressured credit card customers to buy costly add-on services like payment protection and credit monitoring.

American Express shares rose 90 cents to $57.76 in afternoon trading Monday.