A delegation from the museum in Amsterdam visited the office of Tokyo's Suginami ward on Saturday, donating the catalogue showing its exhibits and a miniature of the Anne Frank House where her family hid during World War II.
The museum will donate 3,400 copies of the catalogue to libraries throughout Japan, a local official said.
More than 300 copies of the diary, or publications containing biographies of Anne Frank, Nazi persecution of Jews and related material have been torn at many public libraries in Japan, news of which sparked alarm amid a rightward shift in the country's politics.
Suginami ward found at least 121 damaged books at 11 of its 13 public libraries, the local office said.
Jan Erik Dubbelman, head of the museum's international department, handed the catalogue to Suginami mayor Ryo Tanaka.
"I also trust that by strengthening and expanding the friendship between Japan and the Anne Frank House and the people in Japan who strive for harmony, this incident will be soon forgotten," he said.
Dozens of related publications donated
Tanaka said since the news was reported the ward had received dozens of related publications given by donors.
The Israeli embassy in Japan has also donated 300 copies of the diary to Tokyo libraries.
Anne Frank, a German Jew born in Frankfurt in 1929, documented her family's experiences hiding in concealed rooms during the German occupation of the Netherlands where they settled in 1933.
They were caught and sent to Nazi concentration camps. Anne and her sister died of typhus in 1945.
Anne's "Diary of a Young Girl" was added to the UN Education, Scientific and Cultural Organization's Memory of the World Register in 2009.
The vandalism spree comes amid criticism of a rightwards shift in Japanese politics under nationalist Prime Minister Shinzo Abe, with a recent volley of provocative comments about Japan's wartime past that have sparked accusations of revisionism by China and South Korea.