I have seen the 60 Minutes interview (March 2020: Dr. Anthony Fauci talks with Dr Jon LaPook about Covid-19) used as proof positive for this. The dialogue goes (transcribed by me. I is the interviewer and F is for Fauci):
F: The masks are important for someone who's infected to prevent them from infecting someone else. Now, when you see people and films from China, South Korea, ... everybody is wearing a mask. Right now, in the United States, people should not be walking around with masks.
I: You're sure of it? Because people are listening really closely to this.
F: Right now there is no reason to be walking around with a mask. When you're in the middle of an outbreak, wearing a mask might make people "feel" a little bit better and it might even block a droplet, but it's not providing the perfect protection that people think that it is. And often there are unintended consequences. People keep fiddling with the mask and they keep touching their face.
I: And can you get some schmutz sort of staying inside there?
F: Of course. But when you think "masks", you should think of healthcare providers needing them and people who are ill. When you look at films of foreign countries and you see 85% of the people wearing masks, that's fine, I'm not against it.
I: But it can lead to a shortage ... of masks.
F: Exactly, that's the point. It could lead to a shortage of masks for the people who really need it.
Emphasized for clarity. A layman's reading of this certainly supports this interpretation. Specifically he says it's 'not providing the perfect protection people think it is'.
Given that 60 Minutes is a popular show for a general audience, it is hard to justify that one should expect more than a layman's interpretation of this.
Please note that question is not whether masks are effective or not, but what was claimed at the time. For effectiveness see another open skeptics question. Nod to LShaver.
For context, The Hill has an article expanding why these statements were made at the time.