This question originally appeared on Quora. 
Answer by Richard Stern, Entrepreneur, Screenwriter, and Cinephile
There are a lot of theories about that line.
One theory posits that the entire murder was staged by Hyman Roth and the Rosatos to turn Frankie and deliver a star witness to the FBI.
Another supposes that Michael indeed did turn on Frankie and hand him over to the Rosatos fearing that he would disrupt the deal with Hyman Roth by continuing to antagonize them.
Yet another maintains that it was simply a gaffe - and that the line should have been read "tell Michael Corleone (WE or I) says hello." Meaning that the hitman believes Michael has already been assassinated or soon will be, and Frankie will say hello to him shortly in hell.
I find none of these particularly satisfying. They all feel a little too flimsy for such a meticulously crafted film.
Instead, I prefer to think that the goal of the Rosatos was to indeed kill Frankie. The line was delivered as a final insult. "Michael Corleone says hello" is a taunt. The Rosatos believe Michael is a sap, easily being controlled by Hyman Roth, and by association, the Rosatos themselves. Michael is weak and easily manipulated in their eyes. He's in their pocket. Frankie's loyalty to Michael is misguided and now has cost him his life.
When Frankie, by chance, survives the assassination attempt. He doesn't believe Michael tried to kill him literally, but he believes Michael's lack of power has left him exposed on the street. As such, he turns to the FBI for protection. It is only when Michael arrives at the Senate hearing with Frankie's brother that Frankie recognizes that Michael not only has power, but is ruthless enough to use it. Not even the US government could protect Frankie (and his family) from Michael's vengeance.