Failed to query facebook user info: Invalid OAuth access token signature

Started from today, site using Drupal for Facebook started to display this text on top of every page:

Failed to query facebook user info: Invalid OAuth access token signature. 190. (logged into facebook as 0)

without any changes in settings.

All the mentioned preliminary steps (recommended prior to submitting an issue) has been performed.

There are 5 records in Drupal logs related to the fb module(s) when I visit any page:

"Notice: Undefined property: stdClass::$id in fb_api_init() (line 344 of /local/www/dev/sites/all/modules/fb/fb.module)."

"Notice: Undefined property: stdClass::$id in fb_api_init() (line 377 of /local/www/dev/sites/all/modules/fb/fb.module)."

"Notice: Undefined property: stdClass::$id in fb_api_init() (line 390 of /local/www/dev/sites/all/modules/fb/fb.module)."

(error) "Failed to query facebook user info: Invalid OAuth access token signature. 190. (logged into facebook as 0)."

"Notice: Undefined offset: 0 in fb_user_get_proxied_email() (line 1178 of /local/www/dev/sites/all/modules/fb/fb_user.module)."

Facebook PHP SDK (v.3.1.1) is used.

What additional info shall I provide to expect this to be handled?
Thanks.