A total of 1,249 people, or 58%, responded to the NHK phone survey last weekend.
Among those who support the Cabinet, 39% say it is better than the alternatives, 25% say they trust Suga, and 20% say the Cabinet represents the party they support.
On the other side of the fence, 34% say the Cabinet is ineffectual, 33% are doubtful on its policies, and 16% say Suga doesn't have their trust.
Violations of anti-coronavirus measures
One possible factor in the poor polling is the revelation that members of the ruling coalition ignored the government's stay-at-home request under its state of emergency.
Three lawmakers from the main ruling Liberal Democratic Party, including Matsumoto Jun, former chairperson of the National Public Safety Commission, were reported to have visited dining and drinking venues until late in Ginza, one of Tokyo's main entertainment districts. They admitted the misconduct and left the party.
In addition, Toyama Kiyohiko, the deputy secretary general of junior coalition partner Komeito, resigned from the Diet after a magazine reported that he had visited a hostess bar in Ginza.
The scandals led some members of the ruling parties to voice concern that the incidents could lower Cabinet approval, and impact the government's ability to implement policies.
A separate blow was contained in a report last week concerning Suga's eldest son who works for a company involved in satellite broadcasting. He reportedly treated four senior communications ministry officials to meals in a possible violation of the National Public Service Ethics Act.
Japan is likely to approve a coronavirus vaccine developed by Pfizer-BioNTech on February 15. Preparations are underway to start administering it soon afterwards.
The survey asked respondents how they feel about the vaccine. A growing number want to get vaccinated: 61%, up 11 percentage points from a month ago. But 28% still do not want to, and 12% are unsure or declined to answer.
Japanese lawmakers have enacted legislation that allows for tougher enforcement of anti-virus rules, including punishment for individuals and businesses that do not comply.
Most people think the revised laws will play a part in reducing the spread of the coronavirus. 8% expect them to be very effective, while 50% believe they will help to some extent. Another 32% say they won't have much impact and 5% say no effect at all.
People have mixed opinions about how the Suga Cabinet is handling COVID-19. A small number, 4%, say the government is doing a very good job, while 14% think it is doing badly. Almost equal numbers have more moderate views, with 40% suggesting the situation is being managed fairly well, and 39% saying the opposite.
Japan's government is planning to hold another meeting of its expert panel this week to consider if there are any regions where the state of emergency can be lifted.
More than 1,200 new coronavirus cases were reported in the country on Monday. The daily tally is declining nationwide.