Jackson accused doctors who have tried to diagnose Trump from afar of performing "tabloid psychiatry".
The White House said today Trump will not leave for a planned weekend in Florida unless a funding bill passes.
Jackson's medical career began when he graduated from medical school at the University of Texas in 1995.
President Donald Trump is in "excellent health", and has no cognitive problems, but should lose some weight through a regimen that includes improving his diet and getting more exercise, the White House physician said Tuesday.
The president - who is 71 and is six feet and three inches tall, weigh 239 pounds (108 kg) - is borderline obese on the BMI, and his cholesterol was high.
The concerns over his weight aside, Jackson said Trump was in excellent health, which he ascribed to good genetics and a lifelong avoidance of tobacco and alcohol.
Our essential brief on culture, the news, and more. I found no reason whatsoever to think the president has any issues whatsoever with his thought process'.
Dr Jackson said he would increase that dose in an effort to get Mr Trump's so-called "bad" cholesterol, or LDL level, below 120; it now is 143.
But Mr Obama played just 26 in his first year in office, with a total of 333 at the end of eight years, according to a count by CBS News White House correspondent Mark Knoller.
"I have no concerns about his cognitive ability", Dr. Ronny Jackson told reporters from the briefing room.
Still, Jackson said Trump acknowledged he'd be healthier if he lost a few pounds by exercising more and eating better.
Washington had been abuzz in recent days with details from a tell-all-style book suggesting everyone in Trump's entourage questions his mental stability.
Trump also will increase his daily dosage of Crestor, Jackson said, with a goal of getting his LDL cholesterol down to below a reading of 120.
The test looks for signs of dementia or Alzheimer's, an incurable, degenerative brain disease, but doesn't assess psychiatric fitness.
Regarding his physical health, he said he had dieted successfully before.
The fast-food-loving Trump praised Jackson, who has served as a physician to previous presidents, but seemed wary of taking the not-so-subtle suggestion to use the White House's exercise facilities.
Trump is now taking several types of daily medication, Jackson wrote, including aspirin; Rosuvastatin to lower cholesterol; Finasteride to aid in the prevention of male pattern hair loss; Ivermectin to treat rosaccea when needed; and a multivitamin product.
Jackson did note that the president "would benefit" from a diet lower in fat and carbohydrates and also more exercise.