Your question asks about "public domain" but these are really the wrong words to use, as a) it's complicated but unlikely that these data are public domain, and b) it might not matter much for what you are asking to do.
If you just want to use the data, I don't know of any law that would make this illegal, even if the data could be considered a copyrightable database (that is, data are not copyrightable, but collections of data can be). Academic convention is of course to cite, and if the primary data in your paper are from some other source you'll end up going quite a bit beyond just a simple citation and likely have to describe specifically where and why you got the data from that source.
If you want to also distribute the data, rather than just your analysis of the data, that's where you could possibly get into trouble if they were indeed deemed a copyrightable collection (which, of course, they might not), were not associated with a license that allowed you to distribute in the manner you would like to distribute, and it would be safest to just get permission. However, you probably do not need to post the data at all if they are freely available, just point others to where they can be found.
This is a good reminder that if you do produce and distribute data you would like others to be able to use to remember that you should include a license with those data to avoid any ambiguity as to whether people can use the data; if there is no license given, it must be assumed that the authors reserve all rights allowed to them. If your preference is that others use your work, let them know by using a license! Note also that even for data that are released as public domain or with a similarly permissive license, academic standards of citation still apply; licenses give you legal rights only, not ethical ones.