The independent pollster Chronicle found that the number of Russians who fully support the invasion has almost halved since February 2023.
Their survey revealed those who favour peace far outnumber pro-war voices, with more Russians supporting the departure of the country's troops from Ukraine than not.
Discussing the findings, the Insitute for the Study of War (ISW) said on Friday the Kremlin was "likely concerned" about how changing attitudes towards the war could affect the 2024 Russian presidential election.
The US-based think tank claimed Vladimir Putin will centre his re-election campaign on "Russia’s alleged domestic stability and increased criticism of the West instead of focusing on the war."
Conducting polls in authoritarian states, like Russia, is notoriously difficult. The Kremlin has criminalised criticism of the war and spends millions on pro-war propaganda, meaning they may not reflect the realities of the situation.
Chronicles, founded by Russian opposition politician Aleksei Miniailo, says its surveys offer an accurate snapshot of public opinion, however.
The Moscow-based research group asked 1,199 adults across Russia a series of questions in a phone poll between 17 and 22 October.
Chronicles' survey revealed that 40% of Russians support the withdrawal of troops from Ukraine without war aims being achieved. This number has remained consistent throughout 2023.
Thirty-three per cent were against exiting Ukraine and wanted the war to continue, though this number has steadily fallen from 47% in February to 39% in July.
One reason why support for the war is falling could be that Russians are increasingly feeling the pinch and seeing a more gloomy future due to the fallout from the invasion, as a separate survey has shown.
Polling by the Chronicle echoed this, finding that 44% of respondents have experienced a decrease in family income.
Putin announced a significant increase in military spending this week, with about 30% of the country's budget directed toward the armed forces in 2024.
The survey also showed how the situation was impacting peoples' lives.
More than half of the Russian population (52%) recently faced anxiety or depression, u from around a third (32%) in March 2022.
Those on lower incomes were more likely to report negative mental effects.