WASHINGTON — “Person. Woman. Man. Camera. TV.”

President Trump again sought to showcase his mental fitness on television by reciting, over and over again in an interview broadcast on Wednesday evening, what he said was a sample cognitive testing sequence.

For the better part of a month, Mr. Trump, 74, has made repeated appearances on Fox News to brag about acing a cognitive test he said he recently took at Walter Reed National Military Medical Center, first with Sean Hannity and again with Chris Wallace on “Fox News Sunday.” All the while, the White House has not disclosed details about when the president underwent the testing or why.

During the most recent interview — an appearance with Marc K. Siegel, a professor of medicine at New York University and a medical analyst for Fox News — Mr. Trump tried to defend his own mental fitness for office by outlining the particulars of the test he said he had taken, and by questioning the acuity of former Vice President Joseph R. Biden Jr., 77, the presumptive Democratic presidential nominee.

“It’s really something that’s been great,” Mr. Trump said, referring to being the president. “But you need stamina. You need physical health, and you need mental health.”

Then Mr. Trump seemed to offer differing timelines for when he had taken the test.

First, the president said that he had asked a physician during a hospital visit “a little less than a year ago” if there was a test he could take to prove his mental acuity to the news media.

It is unclear when that visit would have occurred: Last month, the White House released a summary of Mr. Trump’s health, but not an annual physical report, and did not explain a highly unusual unannounced visit last fall to Walter Reed. The summary also did not indicate whether he had undergone cognitive testing.

Then, Mr. Trump said that he had asked Dr. Ronny L. Jackson, who has not been his physician since 2018, if there was an acuity test he could take. That year — after the book “Fire and Fury” described some of Mr. Trump’s advisers questioning his fitness for office — Dr. Jackson said that the president had received a score of 30 out of 30 on the Montreal Cognitive Assessment.

That test, also called the MOCA, has been criticized by experts as too blunt an instrument that does not rule out declines in reasoning or memory, or difficulties with planning or judgment.

“I said to the doctor, it was Dr. Ronny Jackson. I said, ‘Is there some kind of a test, an acuity test?’” Mr. Trump recalled on Wednesday. “And he said, ‘There actually is,’ and he named it, whatever it might be.”

Then the president elaborated for several minutes.

“It was 30 to 35 questions,” Mr. Trump said. “The first questions are very easy. The last questions are much more difficult. Like a memory question. It’s, like, you’ll go: Person. Woman. Man. Camera. TV. So they say, ‘Could you repeat that?’ So I said, ‘Yeah. It’s: Person. Woman. Man. Camera. TV.’”

“‘OK, that’s very good. If you get it in order you get extra points,’” Mr. Trump said a doctor told him. “OK, now he’s asking you other questions, other questions, and then, 10 minutes, 15, 20 minutes later they say, ‘Remember that first question — not the first — but the 10th question? Give us that again. Can you do that again?’”

“And you go: ‘Person. Woman. Man. Camera. TV,’” Mr. Trump said. “If you get it in order, you get extra points.”

“They said nobody gets it in order,” Mr. Trump said. “It’s actually not that easy, but for me, it was easy. And that’s not an easy question. In other words, they ask it to you, they give you five names and you have to repeat ’em. And that’s OK. If you repeat ’em out of order, it’s OK, but, you know, it’s not as good. But when you go back about 20, 25 minutes later and they say go back to that — they don’t tell you this — ‘Go back to that question and repeat ’em, can you do it?’ And you go: ‘Person. Woman. Man. Camera. TV.’

“They say, ‘That’s amazing. How did you do that?’” Mr. Trump continued. “I do it because I have, like, a good memory, because I’m cognitively there. Now, Joe should take that test, because something’s going on. And, and, I say this with respect. I mean — going to probably happen to all of us, right? You know? It’s going to happen.”

Mr. Siegel did not ask follow-up questions.

In an interview broadcast on Sunday, when told that Mr. Biden was chosen in a Fox poll as the more mentally sound candidate, Mr. Trump disputed that finding and defended his cognitive test results to Mr. Wallace, who said he had taken the same test that the president had boasted about acing. Mr. Wallace pointed out that one of the questions asked to identify an elephant.

“It’s all misrepresentation,” Mr. Trump said. “Because, yes, the first few questions are easy, but I’ll bet you couldn’t even answer the last five questions. I’ll bet you couldn’t. They get very hard, the last five questions.”

In another portion of the Wednesday interview, he defended his track record as president during the pandemic, reiterating a call for Americans to wear masks to combat the coronavirus.

But Mr. Trump appeared to shift away from more sober assessments he has delivered about the pandemic, which has killed more than 143,000 Americans, by saying that coronavirus testing was “overrated” and “makes us look bad.”

He then accused Democrats of sounding the alarm over a virus for political reasons.

“Watch,” Mr. Trump said, “on Nov. 4, everything will open up.”