"We would like to face historical facts in a humble manner and we would like also to pass on the lessons and facts of history to the next generation," Abe said during the visit to the Jewish girl's former hideout.
"By doing so I wish to encourage peace in the entire international community," he told journalists, stood in front of photographs of Anne Frank.
Abe is in The Netherlands for a Nuclear Security Summit (NSS) and a Group of Seven meeting on the crisis in Ukraine, as well as a much-anticipated mini-summit with South Korea's Park, hosted by US President Barack Obama after the NSS.
Relations with South Korea are at their lowest ebb in years, mired in emotive issues linked to Japan's 1910-45 colonial rule and a territorial dispute, as well as Japan's use of "comfort women" in wartime brothels.
The three-way meeting -- designed to discuss North Korean threats -- is considered a diplomatic breakthrough as Abe and Park have never held a formal summit.
In Amsterdam, Abe noted the "deep connection" between Japan and the Anne Frank diary, and the fact that many Japanese visit the museum.
"When we look back at the 20th century it is fair to say that it was the century characterised by the violation of basic human rights," Abe said.
"And looking ahead to the many years of the 21st century I would like to ensure that we will never see the same things happening, and I share the responsibility of realising this goal."
Abe's visit to the Anne Frank house came after a man was arrested recently for vandalising copies of her diary in Tokyo libraries, although officials said the visit was not directly connected.
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 where Anne and her sister died of typhus in 1945.
Anne's "Diary of a Young Girl" was added to UNESCO's Memory of the World Register in 2009. The Anne Frank House is a dedicated museum open to the public.
More than 300 copies of the diary, or publications about Anne Frank, the Nazi persecution of Jews and related material, were found with their pages torn at many public libraries in Japan last month.
Tokyo police have arrested the 36-year-old man without indicating a motive for the crime or identifying the suspect, who they said has admitted to the vandalism.
Abe described the vandalism as "regrettable".
"The authorities are looking at his motivations. I hope we won't see similar occurrences like this in the future," he said, before heading to The Hague.