The president pushed hydroxychloroquine after it was championed by Home Depot co-founder Bernard Marcus, who donated $7 million to his 2016 campaign.
Hydroxychloroquine has not been shown to be effective against the coronavirus and may even lead to fatal side effects.
Robert Wilkie accused the union of playing politics after one leader said lack of pay could lead to veterans' suicides.
Trump's Veterans Affairs secretary referred to Jefferson Davis as an "exceptional man in an exceptional age."
The VA also reported fewer hospitals earning the lowest one-star ratings.
The department has been paralyzed by infighting over the role of private care for veterans.
"He doesn't know this yet," Trump admitted.