Atheists do not always assert that God does not exist. There are two broad categories of atheism:

“Positive” (or “strong” or “hard”) atheism and “Negative” (or “weak” or “soft”) atheism.

A “Positive atheist” will say “God X does not exist”, whereas a “Negative atheist” will say “I do not believe God X exists” – there is a subtle but important difference.

–This is from atheist Adrian Barnett’s website.