In a statement Usakovs said "material concerning public expenditure published in this week's issue contains lies, fictions and distorted information.
"If the publication will not correct the false information, the local government will take the matter to the courts."
The latest edition of the magazine, which has in the past exposed many cases of sharp practice in high places, was always likely to raise Usakovs' hackles, featuring as it does an image of an apparently naked mayor on its front cover along with the headline: "How close to financial ruin is Usakovs' Riga?"
The magazine alleges that the city's financial state is more parlous than official budget figures would suggest.
Uskovs, himself a former journalist, has in the past won several cases in court after objecting to articles published about him personally and his administration.
In a tweet Friday, Usakovs alleged there was a political edge to the allegations, describing saying the journalists involved represented 'Vienotiba' (Unity) one of the three ruling political parties and accused them of hiding behind anonymous sources.