Though Michael says to Fredo, "Roth wants me out," Michael is the one who wants Roth out. Roth and Vito Corleone had been partners, but only in the Prohibition-era booze business, as Roth pointedly reminds Michael several times. But Michael had been greedily horning in on Roth's Western gambling empire even before Vito died. The first business deal we see Michael involved in when he returned from Sicily was to push Moe Green, Roth's best friend, out of his Las Vegas hotel; later he had Moe killed because he resisted. By late 1958, when we first meet Hyman Roth, Michael has moved his entire operation to Lake Tahoe, owns three hotels in Nevada, and is about to force Meyer Klingman out of a fourth hotel, owned by Roth and the Lakeville Road Boys. And it's obvious that Michael has designs on Roth's Havana gaming empire. Small wonder Roth feels threatened!

Roth planned to kill Michael at Anthony's confirmation party because he knew Pentangeli would be there, contentious about Michael supporting Roth and the Rosato brothers. Pentangeli would have a perfect motive to kill Michael, and would make a perfect fall guy. When the hit on Michael failed, Roth went to Plan B: Invite Michael to Havana, anoint him as Roth's successor in front of witnesses, wheedle $2 million out of Michael, and have his pals in the Cuban government assassinate Michael.

As for Carmine Rosato’s famous line as he was garroting Frankie: “Michael Corleone says hello”: Not even Roth was clever enough to have bet his life on a split-second-timed plot to turn Frankie against Michael. Why would he even try, when he already had Michael in his killing-bottle in Havana? The simplest explanation is one that has been uncovered by Godfather scholars in an interview with Danny Aiello, who played Carmine Rosato. Aiello admits he ad-libbed the famous line, and Francis Coppola, for some reason (probably inadvertence), permitted the ad-lib to remain in the film, to the eternal bafflement of Godfather fans. But it’s also possible that Coppola, the most careful of directors, allowed it to remain because it fit the plot, even though Carmine intended to kill Frankie all along. “Michael Corleone says hello” was intended not for Frankie—but for Richie, the bartender, whose ginmill was being used to set up Frankie.
It’s obvious that Richie is a “civilian,” not a Made Man, and he’s nervous as hell about his bar being used for a murder (“Carmine, NO, not HERE!” he screams after the cop enters and Rosato draws his gun). Carmine knows that Richie might be squeezed by the cops investigating Frankie’s murder. Richie would be too fearful of Carmine to identify him as the killer. Still, as a civilian, Richie is not bound by the code of omerta. So Carmine hands Richie something he can give the cops so that Richie can get off the hook: “The murderers said, ‘Michael Corleone says hello.’ ” That line would set the police after Michael, and would be picked up by the press-- another nail into the coffin of Michael Corleone’s “legitimacy.” Clever Roth!