NEW YORK — American General Financial Group, a Houston insurance giant and subprime mortgage lender that has agreed to merge with American International Group, will stop offering single-premium credit insurance on its loans by the end of next month.

“By taking this step AGF is responding to the current industry and regulatory environment,” said Ernest T. Patrikis, AIG’s senior vice president and general counsel, in a letter dated Thursday to the New York State Banking Department to counter criticism from Inner City Press, a Bronx consumer group

He wrote that American General intends to offer credit insurance on a monthly basis as soon as it has the “system capability and regulatory approvals to do so,” and that as a result some customers in the interim period may not be able to get credit insurance on their loans.

American General’s move follows similar announcements this summer by CitiFinancial, the subprime unit of Citigroup Inc., and by Household International Inc. of Prospect Heights, Ill.

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