I will reserve comment to see if Trump comes up with any proof.
Best course of action.
He needs to show/produce proof and/or instruct the justice department to investigate the matter. If he immediately and professionally does the latter, it isn't really necessary for the former other than he chose to make this an issue being fought in the court of public opinion versus through legal channels.
And that really is the point here. Trump brought the charge to the court of public opinion, so of course the public will weigh in and discuss evidence (or lack thereof), trustworthiness, etc.
If the case wasn't made in the court of public opinion and instead, through legal channels, the burden of proof, and the consequence of said actions, would be much higher.
Let's see what he does.
Most should at least admit though, his tweets are unprofessional and childish.