A bench of Justices Ranjan Gogoi and R Banumathi have asked the states to reply within two weeks as to what steps have been taken to make the appointment.
The 12 states - Jammu and Kashmir, Manipur, Meghalaya, Mizoram, Nagaland, Puducherry, Tamil Nadu, Telangana, Tripura, Arunachal Pradesh, Delhi and West Bengal - have also been asked to specify the reason for delay or non-appointment of Lokayukta.
Advocate and Delhi BJP leader Ashwini Kumar Upadhyay, who filed the plea in court, claimed that many state governments are "deliberately weakening" the Lokayukta by not providing adequate infrastructure, sufficient budget and workforce.
Section 63 of the Lokpal and Lokayuktas Act, 2013, states that every state shall establish a body to be known as the Lokayukta.
(with inputs from agencies)