The Wikipedia article on Japanese literature opens with the following sentences about the influence of other cultures and bodies of literature on the (nascent?) Japanese literature:
Early works of Japanese literature were heavily influenced by cultural contact with China and Chinese literature, and were often written in Classical Chinese. Indian literature also had an influence through the spread of Buddhism in Japan.
No citation is given for either of these sentences. More detail is provided further down the page about the influence of Chinese literature and writing on the development of Japanese literature, but nothing more is said about Indian literature, and the only other mentions of Buddhism in that page don't seem relevant to this claim. There's almost no detail in the given sentence, not even about the time period when this influence supposedly emerged.
What was the influence of Indian literature on the development of Japanese literature? Well, firstly, what is meant by "Indian literature", since India has so many languages and cultures and has had for centuries? Then, what evidence of this influence can be seen in Japanese literature, and from what era?