I am interested in learning whether this is also true of a US president who is in office at that time.
Yes, the President of the United States has a passport, according to the Washington Post.
However, it is not the kind of ordinary passport that most Americans would get, but rather, it is a Diplomatic Passport.
Does a sitting US president require a passport to travel internationally?
The other answer is correct to say that the president has a passport, and in fact the president probably has at least two because he would retain his ordinary passport when the diplomatic passport was issued. But the question is whether the president requires a passport to travel internationally, and the answer to that is no. Any country that wants to receive the US president, or any other head of state, will do that whether the person has a passport or not.