zaichik, thanks for help. However it is not working exactly as expected - all requests are rewritten to / - it is impossible to reach /balancer. This is caused by the first line of your code - all requests match it.
Finally I made it a little different way, which is not 100% I wanted at the beginning, but it is satisfactory enough for me:
Code:
RewriteEngine On
RewriteCond %{REQUEST_URI} !^/balancer$
RewriteRule ^/(.*)$ /index.html [L]
All requests except those targeting /balancer are redirected to /index.html.