Information about the president's health is usually released to the public after the test.
A routine annual affair for every United States president, Trump's medical checkup is being widely reported and has drawn media attention in view of his political opponents raising questions about his health.
But he said the President's comments were "not shocking", adding: "They're not even really surprising".
"Calling the president "mentally ill" in order to insult or undermine him causes actual harm to people with mental health disabilities", the group said in a statement.
"Americans should know whether their president has the energy to stay focused through a long workday and the chances that a significant health issue could compromise the executive office in the years to come".
Such questions about mental fitness, which for other presidents have largely remained out of the public realm, will not be answered by today's exam.
We'll check "what their lifestyle habits are, which is very important in looking for chronic diseases", she said.
President Donald Trump's physician on Friday declared him in "excellent health" after his first known physical checkup since his inauguration almost one year ago.
Former President Barack Obama's exam included a summary of his neurological function, stating "his cranial nerves, cerebellar function, motor function, and sensory system all normal".
Doctors who have performed presidential physicals said the task of releasing information that is ordinarily bound by strict privacy rules can prove daunting.
Trump's physical will be among the most closely scrutinized of any president in decades, perhaps since Ronald Reagan, who was wounded in a 1981 assassination attempt and also suffered from Alzheimer's disease while still in office, according to his youngest son, Ron Reagan.
No, there is no requirement that a person has to have a medical exam of any kind while they serve as president. The association suggests players walk the golf course instead of renting a golf cart. George W. Bush traded running for mountain biking to preserve his knees. Bill Clinton, despite a weight problem, could run at an 8-minute-mile pace.