When I remove the requestQuery.add() line - all works fine except absence of network data. After adding requestQuery.add() - I'm getting this:
Traceback:
08-29 18:15:53.071    6305-7075/? E/dalvikvm-heap﹕ Out of memory on a 840969348-byte allocation.
    08-29 18:15:53.141    6305-7075/? E/AndroidRuntime﹕ FATAL EXCEPTION: Thread-27227
        java.lang.OutOfMemoryError
                at com.android.volley.toolbox.DiskBasedCache.streamToBytes(DiskBasedCache.java:322)
                at com.android.volley.toolbox.DiskBasedCache.readString(DiskBasedCache.java:540)
                at com.android.volley.toolbox.DiskBasedCache.readStringStringMap(DiskBasedCache.java:562)
                at com.android.volley.toolbox.DiskBasedCache$CacheHeader.readHeader(DiskBasedCache.java:403)
                at com.android.volley.toolbox.DiskBasedCache.initialize(DiskBasedCache.java:156)
                at com.android.volley.CacheDispatcher.run(CacheDispatcher.java:84)
Here's the code I have:
public class DataReceiver {
    public static void initializeCountriesListUpdate(String urlString, final Context context) throws IOException {
        RequestQueue requestQueue = Volley.newRequestQueue(context);
        JsonObjectRequest jsonObjectRequest = new JsonObjectRequest(Request.Method.GET, urlString,
                new Response.Listener<JSONObject>() {
                    @Override
                    public void onResponse(JSONObject response) {
                        try {
                            ArrayList<Country> countriesList = JsonParser.getCountriesFromJson(response, context);
                            ((CountriesListActivity)context).updateCountriesList(countriesList);
                            ((CountriesListActivity)context).progressDialog.hide();
                            ((CountriesListActivity)context).progressDialog.dismiss();
                        } catch (JSONException e) {
                            e.printStackTrace();
                        }
                    }
                }, new Response.ErrorListener() {
            @Override
            public void onErrorResponse(VolleyError error) {
                Log.e("NetworkManager", "Cannot resolve data from the server");
            }
        });
        VolleySingleton.getInstance().getRequestQueue().add(jsonObjectRequest);
    }
UPD1:
I tried to add
    android:hardwareAccelerated="false"
    android:largeHeap="true"
to Manifest, but it doesn't helped.