Kishida took office last September and will be leading his ruling Liberal Democratic Party (LDP) through an election for the upper house of parliament on July 10.
Support has been consistently high, with voters largely approving of his handling of the coronavirus pandemic and his response to Russia's attacks in Ukraine.
But support edged down 2.1 points from the previous month's survey to 48.1 percent, slipping below 50 percent for the first time in four months, according to the survey conducted earlier this week by Jiji News Agency.
More than half of respondents, at 54.1 percent, said they were critical of his government's handling of a wave of price rises driven by the Russian attacks and the fall of the Japanese yen to a 24-year-low, feeling not enough has been done.
The results echo a survey by Kyodo News Agency earlier this week that found 64.1 percent of respondents did not support Kishida's handling of price hikes, while his support slipped 4.6 points to 56.9 percent.
Although Japan's economy is expected to grow an annualised 4.1 percent this quarter as the coronavirus pandemic fades, a slide in the yen is threatening to hurt consumer sentiment as higher fuel and food costs inflict pain on households.
But the LDP is still widely expected to win the election, due largely to disarray among opposition parties.