Reid's spokesman, Jonathan Franks, announced the news.
The submitted application, as specified, requires the UN to recognize the illegality of Reed's detention in Russia and the violation of his rights.
"The petition also seeks compensation from Russia for violating Reed's rights," Franks said on Twitter.
Earlier, Russian Ambassador to the United States Anatoly Antonov said that the rescue of Russians from American prisons is a key task for Russian diplomats.
He said that Russians in American prisons are denied medical care and the provision of necessary medicines.
According to Antonov, in this way there is a violation of international obligations by the United States.
Earlier, the wife of Victor Bout, Alla, a prisoner in an American prison, reported a sharp deterioration in his health in an American prison.
In May, the Russian embassy in Washington said that Russian citizens Viktor Bout and Roman Seleznev, held in US prisons, had been denied medical care.