Medvedev, who parrots Putin's rhetoric regarding the Russian attack upon Ukraine, said "It is so important to achieve all the goals of the special military operation. To push back the borders that threaten our country as far as possible, even if they are the borders of Poland."
"Victory will be achieved. We all want it to happen as soon as possible. And that day will come," said Medvedev. He predicted that tough negotiations with Ukraine and the West would follow that would culminate in "some kind of agreement."
But he said that deal would lack what he called "fundamental agreements on real borders" and not amount to an over-arching European security pact, making it vital for Russia to extend its own borders now.
Medvedev, who is now deputy chairman of Russia's Security Council, made the comments in a message on his Telegram account exactly a year after Russia sent tens of thousands of troops into Ukraine in what it called a "special military operation" and claims was done to protect Russian speakers and ensure its own security.
Poland shares long eastern borders with Ukraine and with Russia's ally Belarus, and a frontier of some 200 km in its northeastern corner with the Russian exclave of Kaliningrad.
Any encroachment on Poland's borders would bring Russia for the first time into direct conflict with NATO. U.S. President Joe Biden pledged in a speech in Warsaw this week to defend "every inch" of NATO territory if it was attacked.
Article Five of the NATO Charter states that an attack upon any NATO member is an attack upon all, and under this agreement, any Russian operation would trigger a unified response, including that of the United States.
Observers say Medvedev's rhetoric could be an indication that he is trying to position himself as a possible successor to Putin should he leave office.