According to the Facebook page of the Anne Frank House, Bieber, 19, toured the museum with his entourage for more than hour on Friday evening and before leaving, he signed a guest book with the following message:
"Truly inspiring to be able to come here. Anne was a great girl. Hopefully she would have been a belieber."
The singer's fans, mostly teen girls, are known as "Beliebers."
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An official statement posted Monday praised the young singer.
"We think it is very positive that he took the time and effort to visit our museum. He was very interested in the story of Anne Frank and stayed for over an hour. We hope that his visit will inspire his fans to learn more about her life and hopefully read the diary," the museum said in an official Facebook post.
Via social media, users said the entry showed disrespect for Frank, who died of typhus in the Bergen-Belsen concentration camp in March 1945.
One person commenting on the museum's Facebook page criticized the singer as being "way too full of himself," adding, Frank is "an important historical figure, so show some respect."
Another wrote: "Glad he went, but the last sentence is VERY self-serving. He missed the lessons of Anne totally."
Yet another said, "Way to use Anne Frank for self-promotion."
"I hope he revisits the museum again once he is older and hopefully wiser and truly understand the messages of peacefulness, humility and respect that are wound within those walls," one woman wrote.
Bieber is in the middle of a European tour and had a concert scheduled in Arnhem in the Netherlands on Saturday night.
BBC correspondent Anna Holligan, based in the Netherlands, wrote on Twitter that she confirmed with the Amsterdam museum's press office that Bieber did write the note in a "special guest book."
There has been no comment from the singer on the museum visit.