After a secret investigation over several years - that used extensive surveillance of communications and wiretaps, including putting listening devices into the homes of the accused - the justice department announced the arrests on Monday.
Sergei Lavrov, Russia's foreign minister, said his country is awaiting an explanation from the US over the arreats.
"The subject was not explained to us. I hope they will explain," Russia's Interfax news agency quoted Lavrov as saying on Tuesday.
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.
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 on Sunday 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.
|Former UK intelligence officer speaks to Al Jazeera about significance of 'spy' arrests
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.
Also charged was an 11th defendant, who allegedly delivered money to the defendants, though he is at large.
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."
The timing of the arrests was notable given the emphasis that Barack Obama, the US president, and his Russian counterpart Dmitri Medvedev have placed on "resetting" US-Russia relations.
The two met just last week at the White House after Medvedev visited California's Silicon Valley, and both leaders attended the G8 and G20 meetings over the weekend in Canada.
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.
|Residents of this New Jersey home were among the 10 arrested on Sunday [AFP]
The court papers cited numerous examples of communications intercepted in the FBI probe that spelled out what they were allegedly trying to do.
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.
In 2009, for example, two of the accused, Richard and Cynthia Murphy, were asked by Moscow to provide information about the US negotiating position on the START arms reduction treaty as well as Afghanistan and the approach Washington would take in dealing with Iran's suspect nuclear programme, ahead of Obama's trip to Russia that summer.
They were also asked to send background on US officials who would be travelling with Obama or involved in foreign policy, and to get their views and learn their "arguments, provisions, means of persuasion to 'lure' [Russia] into co-operation in US interests", according to the court documents.
The papers also described one defendant's contact with a prominent New York-based financier who was active in politics and another's conversations with an unidentified man who worked "on issues of strategic planning related to nuclear weapon development" at a US government research facility.