The unknown individual is heard swearing on a zoom call attended by around 50 others on Thursday (April 29).
The clip, recorded during the City of Edinburgh Council's monthly meeting, was shared on social media by Edinburgh Conservative councillor Mark Brown.
At one stage in the meeting, Tory Cllr Jim Campbell speaks to the group about an issue which would require the council's advice.
In the clip, he can be heard saying: "It would benefit from the council giving some guidance on how to proceed."
In the background, an unknown individual can be heard saying “oh for f***s sake”.
Sharing the footage on Twitter, Cllr Brown wrote: “Clearly someone was frustrated at my @EdinburghTories colleague Jim Campbell’s contribution at full Council meeting today. Wonder who it could be..”
Edinburgh City Council has been approached for comment.