Are you adding any of your own content to the pages that feature these syndicated press releases? If you add some of your own content around the press releases on the page, so almost as if you are quoting it, some people argue this can sometimes navigate the issue - but you need to be really adding more of your own content to the page as compared to the original source, and possibly adding a link to credit it.
However, this is still not really ideal and no guarantee that your site won't get impacted because of duplicate content, and I would try to avoid using syndicated content at all, or blocking the pages from being counted as duplicate content.
You can do this in too ways:
You can use a cross-domain canonical tag on pages in question. This is where you define a canonical tag in the page's source code referencing the original source of the press release:
<link rel="canonical" href="http://www.example.com/original-source-of-press-release" />
This indicates to Google that you are aware the page contains duplicate content, so not to count it during indexing. However this will mean the page on your site will over time be removed from the search results.
The 2nd option is to noindex the page so that Google no longer indexes the page and won't count it as duplicate content. The best way to to this is add the following robots meta tag:
<META NAME="ROBOTS" CONTENT="NOINDEX, FOLLOW">
This means that Google can still freely crawl the page, but will no longer indexed it, meaning it will be removed from the search results.