Barclaycard retaliated by bringing out two new cards, a Gold card for high spenders and a Sense card aimed at more cautious customers.
The Gold card has a minimum credit limit of £2,500, while the Sense card has a maximum credit limit of £500.
Interest rates on the Gold card, available to existing customers by invitation only, will be 20.9 per cent APR. The Sense card charges 21.6 per cent APR.
Shaun Powell, Barclaycard's commercial director, said its card launches followed extensive research showing that potential users have widely differing needs.
"Consumers are not uniform or typical in their attitudes to credit cards. They have very definite and different demands when it comes to their ideal card," he added.
With Amex's new card, cardholders spending £1,000 or more in one year will pay 16.7 per cent APR. Those spending less than that pay 20.9 per cent APR.
John Crewe, president of American Express's consumer services group, said: "We believe we have created a compelling new product. We are looking at an approach which will allow customers in future to tailor their card to their requirements."
American Express yesterday claimed that its charges would allow savings of £52 a year compared to Barclaycard's standard Visa or MasterCard, on an average £1,000 annual line of credit.
Its figures include the waiver of a £20 yearly card fee, available to all new applicants for the first 12 months. American Express has chosen to include Barclaycard's £10 annual fee.
Existing charge-card holders will have the £20 annual fee waived for life if they apply for the new card.
Users of the American Express credit card will also be eligible for its loyalty scheme, which entitles members to free flights, hotels and other entertainments.
A company spokeswoman added that new cards aimed at further market niches are planned over the next 18 months.
The two issuers' launches are the latest in a series aimed at capturing different slices of the credit card market. They follow launches 18 months ago of the GM Card and Ford Barclaycard, which was aimed at potential car buyers.
For those who prefer a low-charging, no-frills service, Royal Bank of Scotland is currently marketing its own low-interest MasterCard, with an APR of just 14.5 per cent and no annual fee.
Save & Prosper charges 14.6 per cent APR for its Robert Fleming Visa and MasterCards, plus a £12 annual fee.
In March, Bank of Scotland boldly went where no other issuer has yet dared to go, by issuing a special card aimed at Star Trek fans.