After inspecting facilities in the Black Sea resort, where some roads are still being completed and construction equipment is strewn across the city, he said there was still work to be done before the Games open on February 7.
"It is not only evident to us, but to all observers too, that tremendous, high-quality work has been done," he told officials involved in organising the Games. "There are things that need to be accomplished, perfected at the final stage."
"The New Year holidays are approaching," he added. "For you and those working on Olympic sites, the New Year will come after the Paralympic Games end on March 17. For you, New Year will be on March 18."
Russia comes to a virtual standstill between December 31 and January 8, with the main family celebrations on New Year's Eve, a tradition that dates to the Soviet Communist era. Many Russians now also celebrate Orthodox Christmas on January 7.
Putin has staked his personal political prestige on staging a successful Olympics and the Games are expected to cost about $50 billion. During a trip to Sochi in September, he criticised failures and delays in preparations.
The former KGB spy said that construction work should be finished on time, including that of the main Fisht stadium where the opening ceremony will be held, and which Putin is expected to visit on Friday. It has not yet been opened.
Some roads near Olympic sites are still being paved and various buildings are still fenced off and surrounded by construction equipment.
Thirteen official sites are being built, including a stadium that can house 40,000 people, plus facilities for ice hockey, skiing, snowboarding and skating. About 120,000 visitors are expected during the two-week Games.
The preparations have been marred by calls abroad to boycott the Games over a Russian law banning the spread of "gay propaganda" among minors, which rights activists say is discriminatory and in breach of Olympic values.
Putin has said several times that gay athletes are welcome in Russia and that no discrimination will be tolerated. He has said the law is needed to protect young people.
Russia also faces security challenges as Sochi is next to its restive North Caucasus region, which is rocked by almost daily violence from a Islamist insurgency rooted into two Chechen wars.
The Olympic torch has also suffered some problems while being carried around Russia. In the latest mishap, a Russian torchbearer's clothing caught fire this week as he carried it through a Siberian city.
(Writing by Alexei Anishchuk, Editing by Timothy Heritage and Mark Trevelyan)
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