"There can be no middle ground for the well-being of our people. We will not be kind," Perfecto Yasay told the opening of the 47-member council's main annual session in Geneva.
"We will not hesitate to destroy criminals who seek the wholesale destruction of our society," he added.
More than 6,500 people have been killed in Duterte's drug war, launched after he took office eight months ago.
Rights groups and the UN have sounded the alarm over the prospect that the state was serially perpetrating extra-judicial killings.
Duterte's highest profile critic at home, Senator Leila de Lima, was arrested last week on drug trafficking charges.
De Lima, a former human rights commissioner, has said she is innocent and her arrest was an act of revenge for her decade-long efforts to expose Duterte as the leader of death squads during his time as mayor of southern Davao city.
The UN rights office said it was "very concerned" about the arrest and was watching the situation "very closely.
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