Irish broadcaster RTE reported officials in Ireland had also asked for consular access to Whelan, who was described as "an Irish citizen."
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Zakharova previously told TASS that Russian officials had granted the U.S. a request for a consular visit with Whelan. The news agency reported Jon Huntsman, the U.S. ambassador to Russia, visited him Wednesday at the Lefortovo pre-trial detention center.
Whelan was born to British parents in Canada and moved to the United States when he was a child, BBC News reported.
"We are giving every support we can, but we don't agree with individuals being used in diplomatic chess games," British Foreign Secretary Jeremy Hunt told BBC News. "Individuals should not be used as pawns of diplomatic leverage. We need to see what these charges are against him and understand whether there is a case or not."
Few details about the crimes Whelan is alleged to have committed have surfaced since his arrest.
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Whelan allegedly had a flash drive with him during his arrest that contained the names of employees of a secret Russian agency, The Washington Post reported. The newspaper cautioned that details surrounding the allegations have been put forth by Rosbalt, a news service "operated by the wife of a former KGB officer close to Russian President Vladimir Putin."
It was not immediately clear what evidence officials had to back up the allegations against Whelan.
Former CIA officer Dan Hoffman, who worked as the agency's chief of station in Moscow, told the Post that it's likely the Russians will distort Whelan's background to support claims that he acted as a spy.
“As with all Russian propaganda, 90 percent of the story is true and the rest is lies,” he told the newspaper.
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Whelan's attorney, Vladimir Zherebenkov, told TASS on Thursday that he had requested bail for his client, who remains jailed in Russia. Zherebenkov said Whelan was in good spirits on Wednesday, despite his arrest.
Whelan enlisted in 1994 as a reservist with the U.S. Marine Corps, the Post reported, citing military records. He deployed twice to Iraq and rose through the ranks to become a staff sergeant before he was convicted in January 2008 of attempted larceny, dereliction of duty, wrongfully using another person's Social Security number and other crimes in a special court-martial, according to the Post. He received a bad-conduct discharge in December 2008, the newspaper reported.
Additional details surrounding the crimes Whelan was convicted of were not immediately available.
Whelan’s arrest came about two weeks after Maria Buttina, a 30-year-old Russian citizen living in Washington D.C., pleaded guilty to conspiracy to act as an illegal foreign agent in the United States. Authorities said she was acting at the direction of a Russian official.