It is the lowest rating for Putin since 2014, before he enjoyed a surge in popularity over the annexation of Crimea from Ukraine.
The survey by the independent Levada Centre found that trust in Putin has fallen nine percentage points since June and a total of 20 percentage points since November 2017.
Thirteen percent of Russians said they did not trust him, according to the latest poll carried out between September 20 and 26.
The veteran Russian leader last week signed into law a bill that will gradually increase the state retirement age to 60 for women and 65 for men, the first such increase since the 1930s.
Most ordinary Russians are deeply opposed to the reforms, which sparked rare street protests.
"People think the government is trying to solve its problems at the public's expense. It has made an attempt to take something people consider to be theirs: pension savings," Levada Centre director Lev Gudkov told the Vedomosti business daily.
He said social tensions have been building since the end of last year because of a variety of factors including a fall in real earnings and rising prices.
While Putin easily won the March presidential election with more than 76 percent of the vote, public discontent about the pension reforms meant "all elements of concern (about him) were lumped together", Gudkov said.
Putin's lowest ever rating in such a Levada poll was in August 2013, when just 30 percent named him as a trusted politician.
He had suffered a long period of decline in support after the 2008 economic crisis and a wave of protests in 2011-12.
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