Speaking after the event, Luke Henderson, co-ordinator for Unite Against Fascism, said: "The march was absolutely fantastic and we were very happy that we had a great turn out.
"Our march had representatives from the many diverse communities that make Edinburgh a vibrant and open city."
Police said that no arrests were made during either demonstration and disruption to the public was kept to a minimum.
Chief Superintendent Malcolm Graham said: "Lothian and Borders Police are well-versed in hosting demonstrations such as these and considerable planning was undertaken along with our various partner agencies to ensure today passed without any problems.
"We will continue to provide a high-visibility presence throughout the city centre today to offer reassurance to the public and deter criminal activity. I would like to thank the public for their assistance and co-operation during this operation."