Mr Duterte said he might ask China and African nations to form another body. He also accused the UN of failing on terrorism, hunger and ending conflicts.
Mr Duterte, elected in May, has sanctioned the killing of traffickers to try to wipe out the drugs trade.
The UN has repeatedly condemned the drive as a violation of human rights.
Some 900 suspected drug traffickers have been killed since Mr Duterte was elected on 9 May.
Duterte: 'Punisher' to president