Vadym Skibitsky, deputy head of Ukraine's military intelligence service, told Germany's Die Welt newspaper that Kyiv wanted to assassinate Putin.
Two women, a journalist and a director of an anti-Kremlin NGO, reported symptoms that suggested possible poisoning.
Dmitry Peskov: "We take an extremely negative view of this. Britain is trying to be one of the leading countries which keeps pumping weapons into Ukraine."
Lukashenko's office declined to comment on the state of his health while Russia denied he was ill.
The group said it was entering politics as an opposition party without any formal or informal instruction from the Kremlin.
As part of its economic response to Russia's invasion, Kyiv has imposed sanctions on Russia.
Kaliningrad, which sits in an exclave that is sandwiched between Lithuania and Poland on the Baltic coast, was known by the German name of Koenigsberg until after World War II.