Michael had no intention of killing Frankie because, as soon as the smoke cleared after the shooting, he was 99% certain that Roth was behind it. "Frank Pentangeli is a dead man" was designed to make Roth believe that Michael was convinced Frankie was the perp.
But, instead of killing Frankie, Michael calls on him. In one of Pacino's best scenes, IMO, he makes it look like he suspects Frankie--then tells Frankie that he wants him to help take his revenge on Roth. Frankie, practically peeing in his pants, nearly passes out with gratitude. "Michael...anything.." he says. "Settle these problems with the Rosato brothers."

It was Michael at his most manipulative: Frankie accepted this dangerous mission, thereby proving his loyalty to Michael and erasing the 1% lingering doubt. If he succeeded, that was one less problem for Michael to worry about. If the Rosatos killed Frankie during his mission, it'd be more proof that Roth was behind the Tahoe shooting. Either way, Michael couldn't miss.

Of course Johnny Ola wanted to know if it was a setup. They expected Michael to kill Frankie, not to send him to meet with the Rosatos. When Roth saw that Michael not only didn't kill Frankie but dispatched him to settle his problem with the Rosatos, Roth knew that Michael no longer suspected Frankie as the would-be Tahoe assassin--meaning that he might suspect Roth. So Roth went to plan B:

--Lure Michael to Cuba with the promise of handing over his Havana gaming empire--but with the real purpose of getting $2 million out of Michael and then having his pals in the Cuban governement whack Michael.
--Have his pals the Rosatos whack Frankie, thereby eliminating Michael's caporegime in NYC and setting up the Rosatos to take over the "olive oil business" after Frankie--and in short order, Michael, was gone.

You should know that the issue of Roth "setting up" Frankie to survive the garroting is one of the most oft-discussed on this board. I and many others here believe that there was no way--repeat, no way--Roth could have engineered Frankie's survival. He intended Frankie to be dead. The cop's intervention was pure happenstance.