Signing statements, which are generally ghostwritten for presidents by Justice Department and White House lawyers, are official documents in which a president lays out his interpretation of new laws and instructs the executive branch to view them the same way.

Once obscure, the practice became controversial under President George W. Bush, who challenged more provisions of new laws than all previous presidents combined — most famously a 2005 ban on torture championed by Senator John McCain, Republican of Arizona. (Democrats are pressing for access to any White House papers of Mr. Trump’s Supreme Court nominee, Brett M. Kavanaugh, related to that statement.)

Mr. McCain is now fighting brain cancer, and Congress named the new military law in his honor. But Mr. Trump pointedly did not mention his name when signing the bill, the latest slight in the long-running acrimony between the two men. Mr. Trump’s signing statement also quoted only part of the bill’s title, evading any acknowledgment of the senator.

Last month, Mr. McCain issued a statement calling Mr. Trump’s Helsinki summit meeting with President Vladimir V. Putin of Russia “one of the most disgraceful performances by an American president in memory.”

The American Bar Association in 2006 took the position that presidents should not use signing statements, but should instead veto legislation if it has constitutional defects so that Congress has an opportunity to override that veto if lawmakers disagree. But presidents of both parties, including Barack Obama, have continued to use them, with current and former executive branch lawyers arguing that the focus should be on the credibility of the legal theories that presidents invoke when they make their objections.