Buryakov appeared in Manhattan federal court without handcuffs and wore dark blue overalls during the 10-minute hearing. Judge Richard Berman remanded him in custody until his next court appearance on March 26.
Alexandra Patchen, a spokeswoman for Buryakov's law firm, Latham and Watkins, said she would not talk about the case.
Prosecutors claim that Buryakov, Igor Sporyshev, 40, and Viktor Podobny, 27, plotted in the United States to gather economic intelligence for Russia's Foreign Intelligence Service's facility and to recruit New York residents in a scheme that started in 2012.
During the period of the alleged plot, Buryakov posed as an employee of a Russian bank, Sporyshev was a Russian trade representative, and Podobny was an attache to Moscow's UN mission, prosecutors say.
Buryakov was arrested in New York in January while Sporyshev and Podobny had left the United States and were not detained.
The case comes amid tensions between the US and Russia that are at their worst since the end of the Cold War. Moscow and Washington accuse each other of backing a military confrontation in eastern Ukraine that has claimed more than 5,400 lives since last April, according to UN estimates.
In January, Russian Foreign Ministry spokesman Alexander Lukashevich accused Washington of detaining Russian citizens without evidence and said the "anti-Russia campaign" would undermine relations between the two countries.
