Naik met the chief minister at Raj Bhawan and held a detailed discussion over the death of journalist Jagendra Singh, an official spokesman stated here.
The Governor said as the incident involved a journalist, it has become a subject of discussion not only in the state but across the country.
Naik said there was a need to instill confidence among people by ensuring a fair inquiry and said that several political parties, journalist associations and other organisations had submitted memoranda to him in connection with the matter.
A delegation of BJP and Congress leaders had yesterday met the Governor demanding dismissal of Minister of State for Backward Classes Welfare Ram Murti Verma, who has been accused of orchestrating the journalist's murder.
Naik also talked of providing proper financial assistance to Singh's family.
Akhilesh said a detailed inquiry was being conducted by IG Bareilly range R K S Rathore and assured the Governor that the probe would be conducted in an impartial, speedy and justifiable manner.
The Allahabad High Court also has directed the state government to file a status report within a week in the matter and has asked government counsel to inform it about the stage of investigation by June 24 along with their objections raised during course of hearing the matter.
Singh was allegedly set on fire by policemen on June 1 during a raid at his house at Vikas Colony in Sadar Bazar, Shahjahanpur, and he died during treatment at a hospital in Lucknow on June 8.