WASHINGTON — At a March visit with doctors and researchers at the Centers for Disease Control and Prevention, the public health agency at the heart of the fight against the coronavirus, President Trump spoke words of praise for the scientific acumen in the building — particularly his own.

“Every one of these doctors said, ‘How do you know so much about this?’ Maybe I have a natural ability,” Mr. Trump said.

It was a striking boast, even amid a grave health crisis in which Mr. Trump has repeatedly contradicted medical experts in favor of his own judgment. But a disregard for scientific advice has been a defining characteristic of Mr. Trump’s administration.

As the nation confronts one of its worst public health disasters in generations, a moment that demands a leader willing to marshal the full might of the American scientific establishment, the White House is occupied by a president whose administration, critics say, has diminished the conclusions of scientists in formulating policy, who personally harbors a suspicion of expert knowledge, and who often puts his political instincts ahead of the facts.