Mr. Trump’s allies point to a bill he signed to improve accountability and overhaul services at the scandal-plagued Veterans Affairs Department. They note that the president signed into law spending plans that will significantly raise federal expenditures on the military and border security. And they say Mr. Trump and the Republican-led Congress worked to methodically reduce the burden of government regulation.

That effort to undo regulation involved 15 new laws, which were the result of an aggressive push to employ a little-used legislative tool to roll back government rules put in place by former President Barack Obama. Those new laws could result in a significant shift in the way government regulates employee benefits, worker safety, the environment, public lands and education.

“These repeal bills are now law, which means those Obama regulations have been struck from the books — forever,” House Speaker Paul D. Ryan said recently.

And legislation is not the only tool presidents can wield to enact their agendas. His aides note that Mr. Trump has used executive orders, such as his ban on travel to the United States for refugees and those living in some Muslim countries, to get around what they say is unprecedented obstruction by Democrats. And he successfully won confirmation of Neil M. Gorsuch to the Supreme Court.

But almost half the other bills Mr. Trump has signed into law are ceremonial or routine. The president includes in his count laws like the one to rename the federal courthouse in Nashville after Fred Thompson, the actor and former senator who died in 2015. Even the Republican leadership in the Senate does not count those kinds of bills when they tally their legislative achievements.

By contrast, Mr. Trump’s tally includes three laws to appoint members to the Smithsonian Board of Regents, another to seek research into better weather reports, and one to require the Department of Homeland Security to manage its fleet of vehicles more efficiently.