Note, the add-on that is installed by kapersky in firefox is NOT your anti-virus. It is a useless add-on, that has features already in Firefox and is only on your computer to gain more money for kapersky. These add-ons are notoriously insecure, cause lots of problems, and do nothing to increase your security.

Regardless what browser you are using or not using, your actual anti-virus (what is actually scanning your computer for malware) is always running in the background, even when you don't even have a browser open. It's always better to update your browser, and remove the useless anti-virus add-on, since updating your browser actually fixes security issues.

According to users on Kaspersky's forum earlier this week, a compatible release is available but you might have to install it manually if auto-updating is not working: http://forum.kaspersky.com/index.php?showtopic=344608