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Putin claims Zelensky doesn't have a right to sign any potential peace deal
(kyivindependent.com)
"Negotiations can be held with anyone," Putin said. "But due to (Zelensky's) illegitimacy he has no right to sign anything. If (Zelensky) wants to take part in talks, I will delegate people who will conduct such talks. But the (key) issue is the ultimate signing of the documents."
The Russian government isn't bound to recognize Zelenskyy, or even the Ukrainian state.
Back when they were trying to annex Finland in the Winter War, they didn't recognize the Finnish government for a while, recognized some puppet for a while.
kagis
The "Finnish Democratic Republic".
https://en.wikipedia.org/wiki/Finnish_Democratic_Republic
The Finnish Democratic Republic was established by Joseph Stalin upon the outbreak of the Winter War and headed by Otto Wille Kuusinen to govern Finland after Soviet conquest.[2][3][4][5] The Finnish Democratic Republic was only recognised by the Soviet Union and nominally operated in Soviet-occupied areas of Finnish Karelia from the de facto capital of Terijoki. The Finnish Democratic Republic was portrayed by the Soviet Union as the official socialist government of Finland capable of restoring peace, but lost favor as the Soviets sought rapprochement with the Finnish Government. The Finnish Democratic Republic was dissolved and merged into the Karelo-Finnish SSR upon the signing of the Moscow Peace Treaty.
However. Yes, they can choose not to recognize Zelenskyy. The thing is that if you actually want to sign a peace treaty, you probably have to recognize the people who are actually in control in the country in question, as they ultimately did with Finland.
Michael Kofman's position, which he's made in several recent discussions, is that he does not expect that the Kremlin currently wants to enter into any sort of peace deal, because it believes that it can prevail militarily. As long as that belief holds, he expects that the Kremlin will probably not be willing to sign off on anything; even if they did, it would be treated as simply a temporary suspension of the war, to be simply broken once it considered Russia's position against Ukraine to be stronger.