J.P. Morgan Chase & Co. has offered to pay about $3 billion as it seeks to settle criminal and civil investigations by federal and state prosecutors into its mortgage-backed-securities activities, according to a person familiar with the discussions.

The Justice Department rejected that sum as billions of dollars too low for the number of cases involved, according to the person. But the discussions have widened to include other investigations of J.P. Morgan, and the final tally could be larger, the person said.

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