The site map urls posted on a Google search return pages with a .html extension and a 404 not found error. The links work fine when the extension .html is removed, but Google continues to receive the wrong information.

Is there a quick solution to fix this problem?

Any help is appreciated.

Hello,
the question is, how do you generate the sitemap.xml file? Or what component do you use for it?

Also you should check when was the last time when Google has loaded your sitemap.xml file? Maybe it was before you made the change?

If your URLs are currently without .html suffix, you just need to make sure the sitemap.xml file is uptodate.
Then you can go to Google Webmaster tools and make Google to reload your sitemap.xml.

To maintaing functionality, you can also create a RewriteRule, that will move all URLs for your site that end with .html to a corresponding URL without this suffix using 301 (Moved Permanently) header.