Support for Kishida's cabinet rose to 65%, up by 4 percentage points from the previous survey a month ago, the newspaper said.
In the latest poll taken from Friday to Sunday, 61% of those surveyed evaluated positively Kishida's anti-coronavirus steps, the highest figure since the Nikkei started asking the public's views on the government's coronavirus response in February 2020.
Amid the global emergence of highly transmissible Omicron variant of coronavirus, Kishida late November announced that Japan was barring entry to foreigners for about a month. Last week, he extended the measure through New Year holidays.
Kishida took office in October, replacing Suga Yoshihide, whose one-year term as prime minister saw his support crumble as COVID-19 surged.
Japan has detected several hundreds new coronavirus cases a day in recent weeks, down sharply from more than 20,000 daily infections in the latest peak in August.