The Kremlin press office said in a statement that Medvedev, sworn in earlier this month, telephoned Yushchenko to 'give an assessment of a number of steps undertaken by the Ukrainian side affecting Russian interests.'
'(Yushchenko's) attention was drawn to the need to stick to the principles of partnership in Russian-Ukrainian relations, not to allow unilateral decisions and steps which violate earlier obligations and agreements,' it said.
The statement did not specify which of the many irritants in ties between the two Slav states Medvedev meant.
Russia has been alarmed by a powerful drive by Ukraine to depart from its traditional dependence on Moscow in favour of closer ties with the West.
Earlier this year Ukraine and Georgia, another pro-Western ex-Soviet state, won an promise from NATO they could eventually join, though without a firm timetable.
Russia considers Georgian and Ukrainian accession to NATO as a threat to its own security.
Moscow is also at odds with Kiev over the future of its military base in the Ukrainian Black Sea port of Sevastopol. Kiev wants the Russian navy to leave after a lease agreement expires in 2017, while Moscow is seeking to extend the deal.
Periodic clashes over gas prices and transit tariffs are also a major problem in relations as Ukraine receives most of its gas from Russia and hosts the biggest transit pipeline to Europe.
Gas rows have eased in the past few months after Kiev settled outstanding debts for gas shipments.
In 2004, Russia backed Yushchenko's pro-Moscow opponent in a presidential election eventually struck down as fraudulent after weeks of peaceful street protests which came to be known as the 'Orange Revolution'.
Many top Russian officials, however, have privately expressed sympathy for Yushchenko in his power struggle with Prime Minister Yulia Tymoshenko, viewed as a more radical pro-Western politician.
The Kremlin statement said Medvedev and Yushchenko agreed to discuss relations during a meeting in Russia's second city of St Petersburg, on the sidelines of an economic forum on June 6-8.