Guterres "believes that human rights are to be upheld in relations to every person everywhere without any kind of discrimination," said UN spokesperson Stephane Dujarric.
"The legislation approved is in clear violation with the principles expressed."
Actor George Clooney calls for boycott of Brunei-owned hotels
The criminal law took effect on Wednesday despite a storm of global criticism from politicians, celebrities and rights groups.
The UN chief "stands clearly against any form of cruel punishment," said Dujarric.
"He stands very much for the protection of rights of all people to be able to be with who they want to be and love who they want to love."
The new code stipulates death by stoning as a punishment for sex between men, while women convicted of having sexual relations with other women face up to 40 strokes of the cane or a maximum 10-year jail term.
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