Which is correct in the following?
I am invited to meet the president.
I am invited to meet with the president.
Both are correct. But there is still a nuance of meaning.
I am invited to meet with the president. ( I have a meeting with the president) - the verb meet is intransitive(without object);
Whereas in your first sentence: the verb "meet" is transitive(with object). ( most likely to mean = be in someone's presence );
Given that you are using the noun "president" and that word combination seems quite a bit more common to me, I would use "to meet with someone".
She and I have decided to meet up(also intransitive) later.
This brings us to the conclusion that some verbs in English can be both intransitive and transitive with little or no difference in meaning at all.
Also, here are some stats from Ngrams:
According to ngrams, "to meet the president" is used slightly more often.