The Kyodo news agency survey was conducted a week after Prime Minister Fumio Kishida fired an aide who said he would not want to live next to lesbian, gay, bisexual or transgender couples and warned people would leave Japan if same-sex marriage was introduced.
Japan is the only country among the Group of Seven nations which does not legally recognize same-sex unions.
The survey showed 64% of respondents were in favor of recognizing same-sex marriage and roughly the same number said a law promoting the understanding of sexual diversity was needed. Just over a quarter of respondents said they were against same-sex marriage.
In November, a Japanese court upheld a ban on same-sex marriage but said a lack of legal protection for same-sex families violated their human rights, a comment welcomed by plantiffs as a step towards aligning Japan with other economically advanced nations.