Police are investigating who ultimately was trying to buy the uranium, which the trio were allegedly selling for $1m.
Police intelligence suggested that the suspects, whose names were not released, but who are all men aged 40, 49 and 51, had originally planned to close the deal sometime between this past Sunday and Wednesday.
The authorities moved in when the sale did not occur as expected.
Kopcik said three other suspects, including a Slovak national identified only as Eugen K, had been detained in the neighbouring Czech Republic in mid-October for allegedly trying to sell fake radioactive materials.
It was unclear to what degree, if any, they played a role in the thwarted uranium sale.
Police said a total of 481 grammes of uranium had been hidden in lead containers, and that a preliminary investigation showed it contained 98.6 per cent uranium-235 - considered to be "weapons-grade".
The arrests heightened long-standing concerns that Eastern Europe is serving as a source of radioactive material.
However, Vitaly Fedchenko, a researcher with the Stockholm International Peace Research Institute, said people should not get the idea that the world is awash in easily obtainable bomb components.
He said: "The danger is definitely there. But there's no reason to panic. Most of the 'buyers' out there are law enforcement agents. And not all of the materials out there are weapons grade."
Over the last few years, Ukrainian authorities have arrested more than a dozen people on suspicion of smuggling or purchasing radioactive materials.
The Vienna-based International Atomic Energy Agency (IAEA), which closely tracks reports of illicit trafficking in radioactive materials, said on Thursday that it was trying to contact Slovak and Hungarian authorities for more information.
Richard Hoskins, the IAEA official who administers the database, said that last year alone the UN nuclear watchdog registered 252 reported cases of radioactive materials that were stolen, missing, smuggled or in the possession of unauthorised individuals.
This was a 385 per cent increase since 2002.
But Hoskins cautioned that the spike probably was due at least in part to better reporting and improved law enforcement efforts.