At the end of Goblet of Fire, Dumbledore was in a room with a bunch of Harry sympathizers, and Cornelius Fudge.
Fudge openly admitted that he was going to reject Dumbledore's suggestions on how to fight Voldemort, didn't believe Harry, and only cared about his Minister post.
It doesn't strike me that Fudge was a powerful wizard.
Why wouldn't Dumbledore simply Imperius the stupid prat, and force him to do the Right Things to prevent further deaths?
(Couldn't have been because he was afraid of power, since he could have commanded Fudge to do anything - resign in favor of Kingsley, do 100% of what Harry tells him, make a press conference and tell everyone Harry was telling the truth).