“See how we have been surrounded by certain machinery and appliances,” Mr Logvinov said on Wednesday.
“I can tell you, a lot of people who spent a long time in Washington got cancer caused by the radiation.”
In response to questions from ABC News, Russia’s embassy in Washington tweeted its apparent support of Mr Logvinov’s claims.
“We are grateful to our colleagues from [Russia’s embassy in Australia] who reminded us about dangerous conditions of our everyday routine in Washington, DC. Nothing can surprise us anymore.”
US State Department spokeswoman Heather Nauert dismissed the Russian accusations as a diversionary tactic.
“Be sceptical of their claims. You notice they’re … always trying to divert attention away from whatever actions that they’re doing,” Ms Nauert said.
“Russia should not be acting like a victim. The only victims in this situation are the two victims in the hospital in the UK right now.”
The sledging between the two former Cold War opponents comes as Russia retaliated against the US for expelling 60 of its diplomats by ordering the same number of Americans leave the country by April 5.
Foreign Minister Sergei Lavrov said Russia would expel a “symmetrical” number of diplomats from other Western governments, including France and Germany, who followed Britain’s initial move to boot out 23 Russian officials.
The ABC has sought more information from the Russian embassy in Washington about the alleged radiation poisoning, of which there are no official reports.
Embassy staff have fallen ill — at the US embassy in Cuba. The FBI and other US agencies are investigating the possibility that 21 diplomats were deliberately targeted by a mysterious “acoustic” attack since October 2016.
It is believed a covert sonic device was used to cause hearing loss and other symptoms, although who was behind the attacks remains unknown.
Several Canadian diplomats also reported similar “attacks”.
Several Russian diplomats have died unexpectedly around the world since November 2016.
On the day of the US presidential election, consular employee Sergei Krivov was found dead at Russia’s New York consulate, the cause of which was reported to be either a head wound or a heart attack.
In February 2017, combative ambassador to the United Nations, Vitaly Churkin, died suddenly in New York after falling ill at work. He was one day away from his 65th birthday.
Mr Krivov and Mr Churkin’s death have not been directly linked to nefarious activities.
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