There is a choice in Activity Reports to Add Contacts to Group, on the top right - so I created a new Group and chose that Group, but there is not a button to click to complete the add. It's not automatic. I'm on Civi 4.6.3.
click on the Preview Report button and you will get the 'Add contacts to group' action. Just tested it on the demo site running CiviCRM 4.6.4 using Safari and Chrome browsers http://d46.demo.civicrm.org/civicrm/report/instance/3
You should start by upgrading to the latest version (4.6.5). Most probably it was a bug that was fixed for 4.6.4. (You can confirm this before upgrading by looking at at the bugs fixed in 4.6.4).