The judge said sentencing will be June 25.
Kuznetsov, a former UN official, was arrested in the United States on September 1, 2005, on money-laundering charges in a scandal that rocked the global organization.
He pleaded not guilty and was released on $1.5 million bail from the Russian government. He has been in New York under house arrest since.
Kuznetsov chaired the United Nations' influential Budget Oversight Committee. He was indicted by a New York court for setting up an offshore company in 2000, allegedly to launder money received from a UN procurement official, who, prosecutors said, had taken bribes from foreign companies seeking contracts with the organization.
Then UN Secretary General Kofi Annan lifted his diplomatic immunity before his arrest.