I have received a warning message claiming that my computer is "under attack".

Those are scam messages.  Are they popping up in a browser window or in some other fashion?

Hello and Welcome to the Webroot Community!
 
THIS IS A SCAM!!  Neither Microsoft nor any other company sends emails, pop ups, or phone calls of any kind advising that you may have a problem.
 
If you clicked anything links, allowed them to remote into your computer, or went to any web sites please submit a Trouble Ticket ASAP.  (Now would be a good idea....)
 
If you would like more information, read on (After submitting that Trouble Ticket.....)
 
NEWS ARTICLE: Tech Support Scams are on the rise.
 
 
Microsoft never issues this type of warning or email or anything of a sort!  Please see the following link for Microsofts official word on this:
http://www.microsoft.com/security/online-privacy/avoid-phone-scams.aspx
 
"Neither Microsoft nor our partners make unsolicited phone calls (also known as cold calls) to charge you for computer security or software fixes.
 
Cybercriminals often use publicly available phone directories so they might know your name and other personal information when they call you. They might even guess what operating system you're using.
 
Once they've gained your trust, they might ask for your user name and password or ask you to go to a website to install software that will let them access your computer to fix it. Once you do this, your computer and your personal information is vulnerable."
 
Also see Avoid scams that use the Microsoft name fraudulently
http://www.microsoft.com/security/online-privacy/msname.aspx 
 
 
For more information here iwhat the United States Federal Trade Commission has to say on the subject::
http://www.consumer.ftc.gov/articles/0346-tech-support-scams
 
"In a recent twist, scam artists are using the phone to try to break into your computer. They call, claiming to be computer techs associated with well-known companies like Microsoft. They say that they’ve detected viruses or other malware on your computer to trick you into giving them remote access or paying for software you don’t need.
 
These scammers take advantage of your reasonable concerns about viruses and other threats. They know that computer users have heard time and again that it’s important to install security software. But the purpose behind their elaborate scheme isn’t to protect your computer; it’s to make money."
 
This scam is common and has been around for quite a while.  Here is a good Webroot Blog article from April 2013 by Threat Researcher Roy Tobin.
http://www.webroot.com/blog/2013/04/30/fake-microsoft-security-scam/
 
Also to help with these issues it's best to install an Ablocker like Adblock Plus for most Browsers: https://adblockplus.org/
 
Thanks,
 
Daniel 😉

They have popped up when I go to gmail.  Haven't  responded to them in any way.  Then ran several virus scans through Webroot which came back clean.

May I ask which Browser you are using as the pop-ups are not from your system but you need to clear all history and cookies and install a good Adblocker so when I find out which Browsers your using then I can give better instructions and suggestions.
 
Thanks,
 
Daniel 😉

I use Explorer as a browser.

Okay can you please do these within the Browser see pictures and make sure you know your account names and passwords? Then go here to install AdBlock Plus: https://adblockplus.org/ and that should fix your issue if not then Submit a Support Ticket and they can help you out and please let us know how it goes!
 
Thanks,
 
Daniel ;)