distinguish

I assume :it means he had had some notion that led him saying that
I suppose :it means he's unsure of what gonna happen to presume (something) to be true without certain knowledge

In any given context they could perhaps be used interchangeably, but, generally speaking I see the difference this way.

"Assume" generally implies that you are taking a given proposition to be true or correct, with or without substantial evidence for it.

"Suppose" often implies that you are withholding judgment on the accuracy of a given proposition, but treating it as valid for the moment. It can also mean to "imagine" something, or take some hypothetical case as being actual, for one purpose or another.