Abe, who became Japan's longest-serving prime minister last year, has been linked to an under-the-table land sale involving a school foundation with connections to his wife, first lady Akie Abe. A local news magazine reported Tuesday that Koizumi, a former mentor to Abe, was urging Abe to resign following corruption scandals.
On Wednesday, Abe appeared before parliament wearing a face mask for the first time in public, while keeping his focus on the coronavirus pandemic.
According to local paper Asahi Shimbun, Abe said he has no intention of resigning from office, in response to a question from the political opposition citing the Koizumi interview.
"Right now I am doing my best to address infections of the new strain of coronavirus," Abe said. "I want to make it clear I do not have the slightest intention of quitting."
Abe's critics say his administration was late to respond to the pandemic and enforced policies to make the number of patients appear smaller before the 2020 Summer Olympics were postponed.
A significant portion of the Japanese public continues to approve of the government's response to the outbreak, however.
According to the Nikkei, a recent survey indicates 47 percent of respondents gave the government high marks, while 44 percent said they view the policies negatively.
Economists in Japan have warned any lockdowns of key regions, including Tokyo, could have a devastating impact.
Economic security may be becoming a fast priority for Tokyo.
Yomiuri Shimbun reported Wednesday Japan's National Security Secretariat launched an economic security policy group.
The NSS assists the prime minister in the areas of diplomacy and security. The new economic department will be in charge of monitoring 5G networks, foreign companies in Japan and advanced military technology.
The group will also bolster economic security policy by cooperating with the United States, according to the report.