Handing out diplomatic credentials in the Kremlin, Medvedev said "no short-term political considerations ... or internal crises can be used to undermine" the longstanding traditions of friendship, mutual respect and trust between Russia and Ukraine.
He said the two nations share hundreds of years of common history and had paid a dear price for their common future.
Relations between the former Soviet republics have soured in recent years over energy prices and Ukraine's pro-Western government seeking integration with the European Union and NATO.
Ukraine is currently experiencing a new political crisis as the ruling coalition of parties led by President Viktor Yushchenko and Prime Minister Yulia Tymoshenko officially split earlier this week amid political infighting and disagreements over Russia's role in the recent Georgia conflict.
The parliament now has to form a new coalition or face an early election, the third since Yushchenko came to power in 2004 strongly supported by Tymoshenko in the street protests known as the "Orange Revolution."
Tymoshenko has recently criticized the president for damaging relations with Russia.