The UUP's Tom Elliott said there should have been arrests after about 20 people in paramilitary-style uniforms led a parade into the city cemetery.
Police have said evidence gathered will be reviewed and prosecutions pursued if offences were committed.
A spokesperson said a proportionate and appropriate policing operation is implemented for all parades.
Earlier, Ulster Unionist Mr Elliott questioned why no arrests were made: "Obviously when you look at the type of parade that it was, when you look at those clad in paramilitary-style uniforms there are questions for police.
"Were they interested in moving in at that time and making any arrests?
"It appears that they weren't and if not are they prepared to do that now?"
About 2,000 people attended the parade organised by Saoradh.
The parade started in the Bogside at Free Derry Corner and made its way into the Creggan estate where a wreath was laid at a republican memorial.
The main oration was given by Paul Duffy, a former republican prisoner, and brother of the prominent dissident Colin Duffy.
The police have responded to criticism following a dissident republican parade in Londonderry on Easter Monday.