The letter is published in today's edition of the "Neutral Turkmenistan" official Russian-language daily.
Called the Palace Of Free Creation, the 10-story building has the shape of an open book and its construction has cost an estimated $17 million.
It was inaugurated on October 17 by Niyazov and Martin Bouygues, the chief executive of the French contractor that has built most of Ashgabat's government buildings.
The Paris-based Reporters Without Borders (RSF) media freedom watchdog on October 19 called the new building a "crude and outrageous provocation."
RSF wrote in a statement: "[Niyazov] is one of the world's worst press freedom predators. No building, however impressive and costly, will change that."
Turkmenistan ranks 165th in the group's press freedom index. RSF says only Eritrea and North Korea have a worse record.
("Neutral Turkmenistan," TDH, Gundogar, rsf.org)