Appearing on CNBC's Squawk Box, Bill Gates had some very complimentary things to say about President-elect Donald Trump.

• Trump has an opportunity to establish "American leadership through innovation."

• "A lot of his message has been about ... where he sees things not as good as he'd like."

• "But in the same way President Kennedy talked about the space mission and got the country behind that, I think whether it's education or stopping epidemics ... [or] in this energy space, there can be a very upbeat message that [Trump's] administration [is] going to organize things, get rid of regulatory barriers, and have American leadership through innovation."

• On power of innovation: "Of course, my whole career has been along those lines. And he was interested in listening to that. And I'm sure there will be further conversation."

Gates had his first telephone conversation with Trump - the first time he had spoken with Trump, though he said they have mutual friends.