Only food from Fukushima, which was hardest hit by the earthquake, tsunami and nuclear meltdown in 2011, remain suspended.
The import of milk, meat, table hen eggs, seafood, fruit and vegetables from Chiba, Ibaraki, Gunma, Kanagawa, Saitama, Tochigi and Tokyo prefectures has resumed.
However, consignments from the areas will have to be accompanied by a certificate of origin as well as a pre-export laboratory report, which certifies the food has been tested for radioactivity and found to be free from contaminants.
"AVA will continue to closely monitor food imports from Japan to ensure that they comply with our requirements for COO, pre- export test reports and freedom from radioactive contaminants. Food imported from Japan that is available in the market is safe for consumption," the authority said.
The decision follows a review by the Singapore authority and assurances from Japan's Ministry of Agriculture, Forestry and Fisheries on the safety of food from Japan.