Abe's latest offering comes just days before U.S. President Barack Obama's three-day visit to Japan from April 23.
Japanese media said Abe will not visit the shrine in person. Fourteen Japanese leaders convicted as war criminals by an Allied tribunal after World War Two are honoured there, along with Japan's war dead.
Visits by Japanese leaders to the Tokyo shrine have outraged China and South Korea, which suffered under Japanese occupation and colonisation in the 20th century. Beijing and Seoul have been highly critical of previous offerings made by Abe.