There is a lot of room for flexibility in interpreting Nietzsche, and unfortunately I do not find him offering anywhere a single, positive characterization of truth and its status.
However, I would not agree that, as the question puts it, “it is well known that Friedrich Nietzsche was very condemnatory of the objective truth.” Nietzsche certainly attacks views about truth and criticizes how the idea of truth is deployed, by both philosophers and laypeople. He offers sharp criticism of those who feel confident they have access to certain truths, and offers cutting analysis of how people use claims of access to important truths as part of claims to power. He especially criticizes claims to truths about value, about what is good and bad. These analyses are a big part of what why Nietzsche is so influential.
Yet, it does not follow from those criticisms that Nietzsche rejects truth or objective truth. Even a criticism of the possibility of objectivity is not a criticism of objective truth. Indeed, when he criticizes positions, he is not shy on leaning on the idea that those positions are wrong—that they are not true. As the Stanford Encyclopedia of Philosophy puts it:
in his equally forceful attacks on, e.g., Christian cosmology, or religious interpretations of natural events, he invokes the conceptual apparatus of truth and falsity, truth and lie, reality and appearance, all the time.
And also, “read[ing] Nietzsche as a global anti-realist — i.e., as claiming that there are no truths or facts about anything, let alone truths about value — … has now been widely discredited.”
More generally, though, consider what follows if you think Nietzsche cannot admit that any claim is more accurate than any other. He cannot say that one kind of life, for instance a life of greatness, is superior to any other kind of life. He cannot say that there are reasons that it's right to admire Beethoven and not to admire servile toadies. He cannot say that certain religious figures engage in deception, misleading their followers. And indeed he does argue those points, not qualified as merely a function of his own perspective, but as a matter of how things are.
Overall, then: Nietzsche does not offer a clear positive articulation of what truth is, and is best known for his remarkable, critical attacks on how we understand and use the idea of truth, but does not offer reasons to think that he does not believe some claims are true and some are false.
(Note, however, that on this point, some of the reflections in the the essay—unpublished during his lifetime—usually titled “On Truth and Lies in a Nonmoral Sense” stand in some tension with most of the rest of his work.)
