Detectives in the North are enquiring into Twitter activity by people purporting to be police officers.
The PSNI warned firm action would be taken if any allegations are substantiated surrounding racist, sectarian, sexist or homophobic behaviour by its staff.
An organisation which represents rank and file officers has reminded its members to be careful online.
A PSNI statement said: "The PSNI is currently carrying out enquiries into Twitter activity connected to persons purporting to be police officers. These enquiries are ongoing.
"The PSNI is not aware of, or are we investigating, many of the allegations published yesterday in an online media article.
"We would appeal to anyone who has evidence of the these matters to report them to us or to the Office of The Police Ombudsman for Northern Ireland.
"The PSNI will not accept any racist, sectarian, sexist or homophobic behaviour from any of our staff.
"All allegations will be investigated and firm action taken if the allegations are substantiated."
The Police Federation for Northern Ireland urged officers to exercise great care and caution on social media.
Chairman Mark Lindsay said there were dangers and pitfalls.
He added: "There is also still a severe threat to our officers and it's essential for their own safety, and the safety of their colleagues, that officers realise the risks and take all necessary precautions to avoid unnecessary attention."
Six PSNI officers have been disciplined for making "unprofessional" and "inappropriate" comments on social media in the last three years. None of those cases related to the current enquiries.
Last year, PSNI Chief Constable George Hamilton apologised to his officers after posting a Saturday night tweet that appeared to dismiss the pressure under which they work.
Mr Hamilton told a fellow PSNI officer and Twitter user: "Dry your eyes, do the job or move on."
The Twitter user had challenged the chief constable's call for people to consider a career in policing, tweeting a picture of a historical recruitment advertisement and pointing out that it was now a more complex job than originally envisaged.
Mr Hamilton later posted a video on Twitter to apologise for causing offence and said he was "hugely proud" of his officers.