Mr. Trump’s former personal lawyer John M. Dowd has marketed himself to convicted felons as someone who could secure pardons because of his close relationship with the president, accepting tens of thousands of dollars from a wealthy felon and advising him and other potential clients to leverage Mr. Trump’s grievances about the justice system.

A onetime top adviser to the Trump campaign was paid $50,000 to help seek a pardon for John Kiriakou, a former C.I.A. officer convicted of illegally disclosing classified information, and agreed to a $50,000 bonus if the president granted it, according to a copy of an agreement.

And Mr. Kiriakou was separately told that Mr. Trump’s personal lawyer Rudolph W. Giuliani could help him secure a pardon for $2 million. Mr. Kiriakou rejected the offer, but an associate, fearing that Mr. Giuliani was illegally selling pardons, alerted the F.B.I. Mr. Giuliani challenged this characterization.