WASHINGTON—Federal prosecutors are actively pursuing criminal cases against executives from Royal Bank of Scotland Group PLC and J.P. Morgan Chase & Co. for allegedly selling flawed mortgage securities, people familiar with the probes said, as the clock ticks down for bringing cases from the 2008 financial crisis.

Officials are working to establish that the bankers ignored warnings from associates that they were packaging too many shaky mortgages into investment offerings and are weighing whether they can prove that constituted...