Russia is now asking for access to the 11 people arrested.
Robert Christopher Metsos, 55, was arrested at Cyprus' Larnaca airport as he tried to leave the island for Budapest early Tuesday, police said.
A magistrate released Metsos on bail of $24,410 to reappear in court within 30 days, when an extradition hearing was due to start.
"Based on the (Interpol) red notice we received, he is wanted for money laundering and espionage," police spokesman Michalis Katsounotos told Reuters.
One of the 10 alleged Russian spies already arrested by the FBI had a fake British passport to help her to travel to and from Russia, it was alleged Tuesday.
A woman calling herself Tracey Lee Ann Foley and posing as a naturalized U.S. citizen traveled to Moscow on the passport forged for her by Russian intelligence services, it was claimed.
The woman was instructed in a coded internet message to pick up the passport in Vienna, sign it and “train yourself to be able to reproduce your signature when necessary."
The message from her handlers at the SVR, the Russian spy agency which succeeded the Soviet KGB, ends: “In the passport you’ll get a memo with recommendations. Pls, destroy the memo after reading. Be well.”
Foley was arrested with her partner Donald Howard Heathfield at their Boston residence Sunday.
The New York Post quoted local residents as saying the couple, who have two teenage sons, never quite fit in the offbeat neighborhood.
"There was no interaction," said neighbor Lila Hexner. "Everything was very nondescript."
The Russian foreign ministry said Tuesday that the U.S. allegations were "groundless and pursue unseemly aims."
"They did not explain what the matter is about. I hope they will," Foreign Minister Sergei Lavrov was quoted as saying during a visit to Jerusalem. "The moment when it was done has been chosen with a special finesse."
The suspects were allegedly carrying out so-called deep-cover assignments on behalf of the Russian Federation, which allegedly provided training in foreign languages, codes and ciphers to the agents, according to The Wall Street Journal.
However, the paper reported that officials said no secrets were compromised or revealed in the alleged plot, and the spy operation seems to have yielded little of value given some of the elaborate methods deployed.
When one couple who called themselves Richard and Cynthia Murphy were arrested in their home in Montclair, N.J., neighbors expressed astonishment that the pair, who they described as “suburbia personified," were accused of spying.
“They couldn’t have been spies,” said one neighbor. “Look what she did with the hydrangeas.”
The Murphys, Vicky Pelaez, a reporter for a Spanish newspaper in New York, and Juan Lazaro, did not challenge bail and were set to appear in court again Thursday, the Fox News Channel reported.
The fifth defendant, named as Anna Chapman, applied for bail and attempted to have all charges dismissed, but lost on both counts. She was set to appear in court again July 27.
Officials also arrested Michael Zottoli, Patricia Mills and Mikhail Semenko in Alexandria, Va.
The arrests, which follow a decade-long investigation, will come as a severe embarrassment to Russian President Dmitry Medvedev, just days after his most cordial meeting yet with U.S. President Barack Obama.
The two ate hamburgers together in Washington and declared the Russian-American relationship “reset” before continuing for more talks in Canada over the weekend.