Democrats abhor many of Mr. Trump’s hard-line immigration and border policies, arguing that they have caused the abuse of children and cruelly perverted long-held American values. But they view some of Mr. Trump’s reported attempts to press reluctant homeland security officials to carry out his more drastic policies as a potentially clearer case of wrongdoing.

In one such episode this spring recounted by people briefed on the conversation, the president told Mr. McAleenan, then the chief border enforcement official, that he should close the southwestern border to migrants and that if he encountered any legal problems, Mr. Trump would just issue a pardon. Mr. McAleenan never took any such action.

Last week, The Washington Post and The New York Times reported that in an effort to speedily construct parts of his border barrier before the 2020 presidential election, Mr. Trump has told aides that they should seize private land and disregard environmental rules. When some raised concerns about the legality of such steps, the president told them he would pardon them if any laws were broken.

Mr. Trump had denied some of the reports, calling The Post’s reporting “another totally Fake story” that was fabricated “only in order to demean and disparage.” And a senior administration official insisted to The Times that Mr. Trump’s comments were a joke.

The Department of Homeland Security and the White House did not immediately reply to requests for comment on Wednesday.