Medvedev, an ally of President Vladimir Putin, forecast on Friday that Russia would be victorious and that some kind of loose agreement would eventually end the fighting.
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.
"That is why 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," said Medvedev.
Poland shares long eastern borders with Ukraine and with Russia's ally Belarus, and a frontier of some 200 km (125 miles) in its northeastern corner with the Russian exclave of Kaliningrad. »