The problem was that when I tried to open any website with Cyrillic font content types the text is not displayed making impossible to open such a websites.
What you have to do is to connect your Kobo to a computer (in my case PC running windows 7) and to find KOBOeReader icon. After navigating to the eReader you have to create folder and name it “fonts”.
On your computer, I find the folder where windows keep its fonts (C:\Windows\Fonts) and I copy all Cyrillic fonts and place them in KOBO fonts folder which you created. Now just disconect your KOBO from your PC and that is it.