UPDATE: The Foreign Police Departments are open to all foreigners again

As of 1 April 2022, the Foreigners’ Police departments are open as follows:

  • Monday, Wednesday, Friday: from 07.30 a.m. to 3.30 p.m. – all applications for granting/renewal of temporary residence, applications for permanent residence and applications for granting/extension of tolerated stay
  • Tuesday, Thursday: from 07.30 a.m. to 3.30 p.m. – applications for residence cards for international truck or bus drivers whose residence has been extended due to a crisis situation and applications for national visas in the interest of the Slovak Republic.

You need an appointment to submit your application. 

Source: https://www.mic.iom.sk/en/news/637-covid-19-measures.html