“This has been the narrative for a while. He saw doing the physical as an opportunity to put some of that to rest,” Dr. Jackson said during a nearly hourlong question-and-answer session in the White House briefing room. “He actively asked me to include that in it, so we did.”

Dr. Jackson said that Mr. Trump received a score of 30 out of 30 on the Montreal Cognitive Assessment, a well-known test regularly used at Walter Reed and other hospitals.

The test is described as a “rapid-screening instrument for mild cognitive dysfunction” that focuses on “attention and concentration, executive functions, memory, language” and other mental skills. It asks patients to repeat a list of spoken words, identify pictures of animals like a lion or a camel, draw a cube or draw a clock face set to a particular time.

Dr. Jackson said the president did “exceedingly well” on the screening test, adding evidence to the doctor’s own assessment that the president has been “very sharp” during numerous interactions he has had with him during the past year.

Psychiatric experts said the brief, 10- to 15-minute screening test is not comprehensive and might not catch all patients with early stages of dementia. Dr. Bandy Lee, the author of “The Dangerous Case of Donald Trump,” which expresses concern about the president’s mental health, said in a brief interview that the president requires a full, detailed neuropsychiatric evaluation.

However, Dr. Jackson said he had observed Mr. Trump closely, often several times a day, for the past year, and was satisfied that the Montreal test is “sensitive enough” to have picked up serious cognitive issues if they were present.

Asked about a much-discussed episode in which the president seemed to slur his words during a televised speech in December about the Middle East, Dr. Jackson said that he and his team of a dozen specialists conducted several tests, including an ultrasound of his carotid arteries, to determine whether there might be a clinical explanation.