"The US has decided to launch the latest stage of its anti-Russian campaign," the foreign ministry said in a statement, accusing Washington of "stoking spy mania".
"We demand an end to this series of provocations by the US security services against representatives of Russia," said the statement from ministry spokesman Alexander Lukashevich.
Lukashevich lashed out at US authorities for providing "no evidence" to back up their claims that the arrested man, banker Evgeny Buryakov, 39, is a spy and demanded his immediate release.
"The hunt for Russian citizens by the American authorities is continuing," Dolgov told TV channel Rossiya 24.
Also Read
"We are going to demand at a high level that the Americans halt actions that breach the rights of our citizens," Dolgov said.
Russia's deputy foreign minister Sergei Ryabkov today held a meeting with US ambassador to Moscow John Tefft to discuss "bilateral" issues, the ministry said.
Buryakov -- an employee at a Manhattan branch of a Russian state-run bank -- was arrested by federal agents in New York yesterday and appeared in court over allegations he was trying to recruit sources and collect economic intelligence.
Sporyshev and Podobnyy were protected by diplomatic immunity and have since left the United States, so have not been arrested. They are charged in absentia, officials said.
Buryakov's detention has rocked already deeply strained relations between Moscow and Washington, which are at their lowest ebb in years over the crisis in Ukraine and war in Syria.
US Attorney General Eric Holder said America was committed "to combating attempts by covert agents to illegally gather intelligence and recruit spies within the United States."
It is the first such case since 10 deep-cover agents including flame-haired Anna Chapman, were arrested in the New York area in 2010. They pleaded guilty and were part of a prisoner swap with Moscow.