Import section / WordPress XML File / Browse disk button doesn’t work

I have a problem importing my blog from WordPress.com. I click Import section, then WordPress, and then I encounter the problem. The Browse button doesn’t work at all, and when I hover over the empty space where I could write down the location of the XML file I would like to upload, cursor turns into loading and doesn’t let me type anything as well.

I don’t know what’s going on. Any ideas how to resolve this?