Wells Fargo & Co, trying to increase its credit card market position, said it is issuing two new credit cards through a partnership with American Express Co in its latest effort to woo more wealthy customers.

The new cards, called Propel 365 and Propel World, offer rewards to consumers who are either big everyday spenders or frequent fliers and who also have another account with Wells Fargo. Cardholders can get up to an extra 50 percent increase in their reward points each year depending on the size of their other accounts at Wells Fargo.

Wells Fargo is looking to bulk up its credit card business, where the bank believes it punches below its weight. It is one of the largest U.S. mortgage and auto lenders, but has a weaker market position in credit cards.

The San Francisco-based bank currently captures only a sliver of affluent consumers' spending. A Wells Fargo executive said in a November investor presentation that around 3 percent of consumers who charge over $100,000 annually on their credit cards do it through a Wells Fargo product.

"We know we're underpenetrated in this customer base, and we're looking to build our share," Beverly Anderson, the head of Wells Fargo's consumer financial services group, told Reuters in an interview.

It's a customer segment where Wells Fargo has some catching up to do. The head of JPMorgan Chase & Co's credit card business, Eileen Serra, said at the bank's February investor day that over half of affluent consumers in the market for a new credit card would consider going with Chase primarily. Wells Fargo did not appear on a slide in an accompanying presentation comparing Chase's popularity against rival issuers.

Wells Fargo announced its agreement with American Express in August 2013. Since the third quarter, the company had been testing its new offerings in five pilot markets around the country.

In another bid to boost its credit-card business, Wells Fargo said in April it would issue and service credit cards for department store Dillard's Inc.