Mr. Trump’s advisers acknowledged that the process was unique to this president, but stressed that he had become personally committed to countering the excesses of the criminal justice system, a mission fueled by his own scalding encounters with investigations since taking office. In addition to his pardons, Mr. Trump in 2018 signed the First Step Act providing sentencing relief for many criminals.

“The president seems to be someone who’s willing to listen to people’s appeals,” said Robert Blagojevich, who lobbied for a commutation for his brother, Rod Blagojevich, the former governor of Illinois sentenced to 14 years for trying to essentially sell the Senate seat vacated by President Barack Obama. “I think he’s just got an antenna to listen to people who have been truly wronged by the system.”

Indeed, Mr. Trump takes personal pleasure in dispensing mercy. He called Patti Blagojevich, who is married to the former governor, right after signing the papers on Tuesday. He likewise called Ricky Munoz to tell him that his wife, Crystal Munoz, was coming home.

Advisers said there is little rhyme or reason to how Mr. Trump chooses clemency recipients. He meets with advisers every few weeks to discuss various cases. Once he makes a decision, he tends to announce them right away, without bothering to draft a communications strategy, reasoning that there is no point in anyone sitting in prison longer than needed.

Mr. Trump recognizes that his friends-and-family approach generates criticism, but has repeatedly cited his 2018 pardon of I. Lewis Libby Jr. as proof that he is willing to absorb attacks that others would not. President George W. Bush refused to pardon Mr. Libby, who served as chief of staff to Vice President Dick Cheney and was convicted of lying to the authorities.

Mr. Trump has known some of those he favored this week for years, including Mr. Kerik and Mr. Milken, the so-called junk bond king who tried at least twice to obtain a pardon from Mr. Bush without success. Mr. Trump called Mr. Milken “a brilliant guy” in his first memoir and has hosted him at his Mar-a-Lago estate in Florida. He called Mr. Kerik “a friend of mine” and “a great guy” in 2004 when Mr. Kerik was forced to withdraw his nomination for Mr. Bush’s secretary of homeland security because of ethics issues.