"Pail Whelan tried to obtain information about students studying at FSB educational facility but was detained," Lukoyanov said at court hearings.
The prosecutor did not mention the name and the location of the school.
Whelan, who is also a citizen of Canada, Ireland and the United Kingdom, was arrested in Russia in December 2018.
Whelan is serving a 16-year jail term in Russia's Mordovia region in line with the Moscow court ruling last June. Whelan has denied the charges against him but did not challenge the verdict in the hope of being deported to the United States.