Neither side would confirm what was discussed during the informal conversation during the opening ceremony in the Russian city of Sochi.
Russia has frozen delivery of a $15 billion bailout program pending the formation of a new government in Kiev.
Mass anti-government protests erupted in Ukraine in late November.
Under pressure from Moscow, Viktor Yanukovych had refused to sign a far-reaching association and trade agreement with the EU.
Amid continuing protests, Viktor Yanukovych has accepted the resignation of PM Mykola Azarov – widely seen as pro-Moscow – and a new prime minister has yet to be nominated.
The meeting between Vladimir Putin and Viktor Yanukovych in Sochi on Friday evening was confirmed by senior Russian and Ukrainian officials.
There was no information about what was discussed, but correspondents speculate it was likely to include the suspended Russian financial package – which Ukraine desperately needs in the face of a sliding currency, dwindling foreign reserves and rising borrowing costs.
Viktor Yanukovych’s meeting with Vladimir Putin follows talks in Kiev last Wednesday between Yanukovych and EU foreign policy chief Catherine Ashton.
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