Mandatory spending cuts by Congress that went into place in 2011 meant that military spending went down in the later years of Mr. Obama’s term. So Mr. Trump can accurately say that he has increased military spending since then.

But under Mr. Trump, the military is also smaller than it was when it peaked during the Obama administration. There are currently 1.2 million active-duty service members, compared with 1.4 million in 2011.

Outlining his plans for the military during a national security speech in Philadelphia in 2016 when he was campaigning for president, Mr. Trump called for an expansion of the military and 75 new ships for the Navy.

Today, the Navy says it will add 10 more ships than what Mr. Obama had planned to build during the same period — from now to 2024.

“Has Trump made the military bigger? No,” said Todd Harrison, a budget expert at the Center for Strategic and International Studies. “Stronger? That’s a qualitative argument, but it’s hard to point to anything that says the military is stronger than it was before he came into office.”

The only technical addition that Mr. Trump can point to is the slight difference in spending, Mr. Harrison said, noting that it is a fine point at best. “He’s accomplished spending more,” he said. “That’s it.”