Japanese news agency said, citing prosecutors, that the court granted their request that 42-year-old Tetsuya Yamagami remain in custody for the entire period of the checks. It did not specify the reasons.
Japanese law reduces the penalty for criminals with insanity.
In July, the Nara District Court granted the prosecution's request for Yamagami to undergo medical checks, including regarding his mental state. The man was placed in the Osaka Detention Center to undergo the procedure.
Abe, 67, was attacked on July 8 in the Japanese city of Nara while he was giving a campaign speech. Yamagami approached the politician from behind and fired two shots from a distance of about 10 meters (33 feet). The attacker told investigators that he had decided to carry out the assassination because of Abe's alleged ties to a religious sect that he claimed had bankrupted his mother. The group has denied having had anything to do with the former prime minister.