Vito had enormous influence over Michael. He was Michael's mentor. The whole killing of the heads of the other families was Vito's idea. RTemember Vito pledged that HE would never be the one to break the peace, a pledge he kept.

The strong influence Vito had over Michael can be seen readilyin two scenes, the first where Michael shakes up the family organization by telling Tom he is "out," and telling Carlo he is going to be his "right hand man" in Vagas. Now we already know the Don didn't like Carlo and he had told Tom never to give him anything important, and never to trust him with information about the family business. He also suspected Carlo was behind the hit on Sonny, yet he went along with the "keep your enemies closer" ploy and he even congratulated Carlo on his "promotion." Meantime, Tom was upset about this and Vito consoles him saying that he never thought Tom was a bad consigliere, but that Santino rest in peace was a bad don. Then,when Tom asks Michael if he can help, and Michael says "You're not a wartime consigliere, Tom, and things could get rough with the move we're trying to make." So Michael clearly is planning all this with his father, and he even says so...he says besides, if I ever need advice who better can I turn to than my father. This is interesting on another level because Michael is showing Tom his implicit trust. Even though Tom is "out" Michael spills the beans that there is going to be another war. So the trust is still there.

Later in the movie, as Vito has become progressively weaker, he is telling Michael about who the traitor will be, and to check the telephones, and Michael gets a little riled, and he tells his father he took care of it, and that he can handle things, and not to worry.

So clearly Michael is doing his father's bidding and is learning all he can before Vito dies.

In the novel there is futher talk about this because Michael makes some kind of comment that Vito's death came a little too soon for Michael to have consilidated the polotical power his father had.