While the majority approved of Putin's presidency, 13 percent of respondents disapproved or refused to answer the question, according to the poll.
It also revealed that 59 percent of those polled currently trust Putin.
Russian Prime Minister Dmitry Medvedev's approval rating is now 64 percent, a 7-percent decline since September 2014.
However, only 19 percent of those surveyed trust Medvedev's while 24 percent trust Defense Minister Sergei Shoigu and 20 percent trust Foreign Minister Sergei Lavrov.
The Russian Lower House of Parliament's approval rating is 50 percent, with 48 percent of respondents disapproving of the MPs' activity, the poll revealed.
The survey was conducted from February 20 to February 23 among 1,600 people across 134 Russian cities. The margin of error is about 3.4 percent.
The Levada Center is an independent non-governmental Russian polling and sociological research organization, which is named after its founder Yuri Levada, the first Russian professor of sociology.