Links my own from posts and pages show up as comments

I write a cooking blog and many of my posts and pages refer to other posts and pages through hyperlinks. After I publish a post or page WP shows that I have new comments. It turns out that some of these are simply from the posts/pages, and I assume initiated by the links.

What do I do with these? I do not want them to be seen on the comment moderation panel nor avaialble as a comment to other viewers.