During the athletes' parade, the 23-strong Ukrainian team was represented by a lone flagbearer in an apparent protest at the presence of Russian troops in Ukraine's Crimean peninsula. The appearance of the flagbearer, biathlete Mykhaylo Tkachenko, drew a roar from the crowd.
The Ukrainian team only announced earlier in the day that it would not boycott the games, but said it could pull out if the Crimea situation escalates.
A lavish ceremony based on the mythical firebird of Russian folklore marked the start of the 11th Winter Paralympics, a 10-day event featuring 547 athletes from 45 countries.
Putin stood at a microphone in front of a capacity crowd at the Fisht Olympic Stadium and announced: "I declare open the Winter Paralympic Games 2014, Sochi."