President of the Winter Olympics Organising Committee Dmitry Chernyshenko presented the logo for the games to the President and gave him a shirt with the new design.
Mr Medvedev also met with President of the International Olympic Committee (IOC) Jacques Rogge and Chairman of the IOC Coordinating Committee Jean-Claude Killy.
Preparations for the Sochi 2014 Winter Olympics and organisation of the Paralympics were discussed at the meeting.
Before the meeting began, Mr Rogge expressed to Mr Medvedev his profound condolences over the tragedy on the Moscow-Petersburg Nevsky Express train.