About 49 suspects, including Russian diplomats and their family members, are accused of reporting false information about their income between 2004 and August 2013 in order to receive free medical services from the US government.
There were 11 people of the total number left in the US when charges were brought against them on December 5.
The suspects included, according to the FBI and media, Russian diplomats, former employees of the Russian permanent mission at the United Nations, staff of the New York consulate and a Russian trade mission.
The suspects allegedly received some $1.5 million in medical insurance payments, according to legal news agency RAPSI.
“Several people from this list have flown to Moscow,” the relative said Tuesday, without specifying how many.
An employee of a Russian diplomatic mission in the United States confirmed that some suspects had left the US.
The Russian Embassy in the US questioned the validity of the charges against the Russian diplomats.
Russia’s Foreign Ministry said, without elaborating, that the Russian side had many complaints against American diplomats in Moscow.
The ministry added, however, that these issues were not made public in Russia.