An official at Yasukuni confirmed the shrine received the offering, a sacred "masakaki" tree, to coincide with an autumn festival, with many lawmakers expected to make their regular pilgrimage tomorrow.
Abe visited the shrine during the festival last year, when he was still in opposition.
Japanese media said two cabinet ministers were likely to go during this year's festival, which runs from today to Sunday.
Yasukuni is a flashpoint in relations between Japan and its Asian neighbours -- particularly China and South Korea -- with disagreements about history badly colouring relations.
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Japanese conservatives say it is natural that they pay homage to people who lost their lives in the service of their country, and say the shrine is no different from Arlington National Cemetery, where the United States honours its war dead.
Moderates dispute this, and are seemingly supported by the US administration, which this month began pushing for a little-known Tokyo cemetery to take its place in an apparent bid to sidestep the corrosive issue.
Abe, who was also prime minister from 2006 to 2007, has stayed away from Yasukuni since he took office in December, amid angry denunciations by China and South Korea of visits by his ministers.
About 100 lawmakers, including three cabinet ministers, went to the shrine on August 15 this year, the anniversary of Japan's surrender in World War II.
Abe sent offerings on the anniversary and for the spring festival in April.
Japan's relations with its two biggest neighbours were bad before Abe came to power, largely as a result of separate territorial disputes.
Tokyo remains at odds with Beijing over a group of islands in South East China Sea and disputes Seoul's claims to own islets in the Sea of Japan (East Sea).