President Trump’s first-term efforts to spur law enforcement officials to pursue his political enemies were haphazard, informal and often hashed out in private.

Now, his demands for investigations are starting to become more formalized through written presidential decrees as he seeks to use the power of public office to punish people and companies he has cast as enemies and silence potential critics.

On Wednesday, Mr. Trump crossed a new line. Flanked by senior aides and cabinet secretaries, the president signed presidential memos that singled out two officials from his first term who had either defied or simply contradicted him. In a clear escalation, he directed the government to examine their actions for any criminal wrongdoing.

The president signed a third order, his most recent attack on law firms for taking clients or hiring former officials he did not like, this time targeting the law firm Susman Godfrey. The firm has led successful defamation suits against news outlets that spread Mr. Trump’s election lies, including a $787.5 million settlement paid by Fox News.

Taken together, the memos send a stark message: To oppose Mr. Trump will mean risking punishment at the hands of the federal government.