The survey said the December rating stood at 25.5 percent, down 15.4 percentage points from the November level.
The Cabinet's disapproval rating rose to 61.3 percent, up 19.1 points from November. The report said 55.7 percent of the respondents disapproved of the Cabinet's postponement of submitting a second extra budget to parliament.
The telephone survey of 1,023 eligible voters was conducted during the weekend, the report said. The respondent's phone numbers were randomly selected by computer.
An approval rating of less than 30 percent in Japan is seen as making it difficult for a government to continue in power, the report said.
The survey said respondents, when asked who they would prefer to be the nation's leader, picked main opposition leader Ichiro Ozawa, who received a 34.5 percent rating, compared to Aso's 33.5 percent.
Aso became prime minister in September.
The delay in submitting the second supplementary budget was seen as showing Aso's lack of consistency in economic policy issues, the report said.
The additional budget, to be submitted next month, is needed to tackle the country's economic and financial problems.