"The secretary general is aware of the visit by the Prime Minister of Japan to the Yasukuni shrine, as well as of a strong reaction to it by China and the Republic of Korea," Ban's spokesperson said in a statement.
"It is highly regrettable that tensions from the past are still plaguing the region. The secretary general has been consistent in urging the countries in the region to come to a common view and understanding of their shared history," the statement added.
The UN chief also said that there is a "need to be sensitive to the feelings of others, especially memory of victims, and focus on building mutual trust and stronger partnership".
"Leaders bear special responsibility in that regard, as the region should strive to be forward-looking and harmonious," he added.
Abe visited the Yasukuni shrine on Thursday. China sees the shrine as a symbol of Japan's past militarism.
It is the first time in seven years, a sitting Japanese Prime Minister has visited the shrine. Former prime minister Junichiro Koizumi paid a visit in August 2006.
Abe's visit has drawn strong opposition from China and South Korea, both of whom suffered Japan's brutal aggression during World War II.
"(We) strongly protest and condemn the Japanese leader's wrongdoing," Qin Gang, Chinese Foreign Ministry spokesperson, said after the visit.
The South Korean government has also officially denounced Abe's visit, the country's news agency reported.