The athletes are five-time world champion speed skater Pavel Kulizhnikov, Olympic short-track speed skating gold medallist Semion Elistratov and 2015 European short-track champion Ekaterina Konstantinova.
"The temporary suspension has been lifted and the sportsmen will be able to train and compete in events," the head of the Russian Skating Union (RSU), Alexei Kravtsov, said in an interview with the R-Sport news agency.
"However, the ISU still has a right to open the case if new evidence appears in subsequent studies that show that the athletes could have taken the banned substance after January 1," he added.
The ISU has also withdrawn the allegations that the three took a banned substance, Kravtsov said, adding: "This means that no prizes will be taken away from the sportsmen."
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The World Anti-Doping Agency (WADA) added meldonium to its list of banned substances in January and 172 athletes, including five-times grand slam tennis champion Maria Sharapova have tested positive for the performance-enhancing drug.
But earlier this month the WADA modified its ban citing a lack of clear scientific information on how quickly the drug clears the human body. The presence of less than one microgram of meldonium in samples taken before March 1 is acceptable, it said.
Kulizhnikov, Elistratov and Konstantinova tested positive on March 18 for meldonium.
Meldonium, manufactured for people suffering from heart problems, helps boost blood flow and increases the amount of oxygen taken in by the body, allowing athletes to recover faster while training. It was widely used in sport before the ban.
(Reporting By Dmitriy Rogovitskiy; Editing by Gareth Jones)
