A brilliant scene showing Michael at his most manipulative:

He came there with an agenda: to first play on Frankie's fear that he suspected him in the Tahoe shooting; and then, taking advantage of Frankie's relief, to maneuver him into a dangerous meeting with the Rosatos. Michael couldn't lose: by agreeing to meet with the Rosatos, Frankie erased whatever tiny, lingering doubt Michael may have had about who was responsible for the Tahoe shooting. If he kissed and made up with the Rosatos, it'd take a worrisome problem off Michael's chest. If the Rosatops atttacked Frankie, it'd not only be further confirmation of Roth's guilt, but it'd give Michael a leg up on Roth if he needed it.

Toward that end: Michael's goal in Havana was to stall Roth on the $2 million long enough to find out who the traitor was in his family. In his last meeting with Roth, he tried to play the Frankie-killed card: after Roth challenged him on why he hadn't brought the bagful of money Fredo brough to Havana, Michael replies, belligerantly, "Who had Frank Pentangeli killed?", as if it was some kind of quid pro quo. But then Roth brilliantly outmaneuvered him with the world-beating Moe Green speech.