Esergepov, the founder and chief editor of the Almaty-based "Alma-Ata Info," was sentenced last year to three years in prison for revealing state secrets in his newspaper in 2008. He says the case against him is politically motivated.
Kazakh authorities declined to release him on parole this year.
Esergepov protested the verdict against him and what he called pressure imposed on him by prison officials after he launched hunger strikes earlier this year.
His wife, Raushan Esergepova, delivered his appeal to Viktoria Tyuleneva, the chief of the Kazkahstan Bureau for Human Rights in Almaty, on July 28. The bureau will forward the appeal to the UN.
Kazakhstan is the current chairman of the Organization for Security and Cooperation in Europe (OSCE).