The 10 suspected spies arrested in Boston, New York, New Jersey and Virginia on Sunday and accused of recruiting political sources and gathering information for the Russian government.
An 11th man was arrested in Cyprus on Tuesday, after immigration officers discovered his name on a stop list, police said.
Christopher Robert Metsos, who was bailed as he awaits an extradition hearing, was identified as a Canadian national but was holding a US passport, police said.
'Infiltrating policymaking circles'
Five of the accused appeared in court in New York on Monday, and were ordered to remain in custody until a July 27 preliminary hearing.
According to court papers unsealed on Monday, the FBI intercepted a message from SVR (Russia's External Intelligence Service) headquarters in Moscow to two of the defendants, describing their main mission as "to search and develop ties in policymaking circles in US".
"The moment when it was done has been chosen with a special finesse"
Russia's foreign minister
They were to "become sufficiently 'Americanised' such that they could gather information about the United States for Russia and can successfully recruit sources who are in, or are able to infiltrate, United States policymaking circles", according to criminal complaints filed in US federal court.
They were not assigned to collect classified, secret information, a justice department official said, but were allegedly tasked to learn about a broad swath of topics including nuclear weapons, US arms control positions, positions on Iran, White House rumours, CIA leadership turnover, the last presidential election, congress and political parties.
Sergei Lavrov, the Russian foreign minister, has called for an explanation of the charges.
"They did not explain what the matter is about. I hope they will," he was quoted as saying by Russian news agencies during a visit to Jerusalem.
"The moment when it was done has been chosen with a special finesse," he said.
Dmitry Medvedev, the Russian president, visited Washington last week and was described by Barack Obama, his US counterpart, as a "solid and reliable partner".
The two met hed talks at the White House after Medvedev had visited California's Silicon Valley, and both leaders attended the G8 and G20 meetings over the weekend in Canada.
'Deep cover spies'
There was no clue in initial court papers about how successful the so-called agents had been, but they were alleged to have been long-term, deep cover spies, some living as couples.
|Obama, left, recently said US-Russia ties had been 'reset' after meeting Medvedev [AFP]
Deep cover agents take civilian jobs with no visible connection to a foreign government, rather than operating from government jobs inside embassies and military missions.
Each of the 10 suspects arrested was charged with conspiracy to act as an agent of a foreign government, which carries a maximum penalty of five years in prison on conviction.
Federal law prohibits individuals from acting as agents of foreign governments within the US without notifying the attorney-general.
Nine of the defendants were also charged with conspiracy to commit money laundering, which carries a maximum 20 years in prison on conviction.
According to the court papers, the defendants had been operating in the US for years, with alleged activities ranging from as far back as 2000 to just Saturday, when undercover FBI agents met two of the accused individuals.
Neave Barker, Al Jazeera's correspondent in Moscow, said serious questions were being asked in Russia over the arrests.
"There are arguments that there are lobbyists operating in Washington DC who act on behalf of foreign countries, so proving espionage for these individuals will be very difficult indeed," he said.
"The argument has also been made that nations friendly to the US, who have had individuals charged with spying in the country, have been sent home without fuss."
FBI agents said in court papers that the defendants communicated with alleged Russian agents using mobile wireless transmissions between laptops computers while they were close to each other.
Intelligence on Obama's foreign policy positions, particularly as they related to Russia, appeared to have been one of the top priorities for the defendants, according to the court filings.