Homosexuality is illegal in Uganda and carries a maximum punishment of life imprisonment.
"I have told the Criminal Investigation Department to look for homosexuals, lock them up and charge them," Tuesday's edition of the government-owned New Vision newspaper quoted him as saying.
Two recent and highly publicized gay marriages in Uganda appeared to prompt Museveni's remarks during a speech Monday to regional legislators meeting in the capital.
"Even the Holy Bible spells it out clearly that God created Adam and Eve as wife and husband, but not men to marry fellow men" the newspaper quoted Museveni as saying.
The Ugandan leader criticized the Universal Declaration of Human Rights, saying it had not been drawn up with the participation of African countries and therefore was "not universal to Africa."
The declaration, while not explicitly mentioning homosexuality, is widely viewed as enshrining the rights of gays and lesbians.