The controversial policies are the latest in a series from the soon-to-be leader, including bans on alcohol and smoking and a curfew for children.
He has also promised to turn the presidential palace into a hospital.
Mr Duterte was nicknamed “The Punisher” for his record as the crime-crushing mayor of the southern town of Davao.
More than 1,000 criminals were killed by security forces in Davao during Mr Duterte’s stewardship.
Speaking at a press conference in the town, Mr Duterte, 71, said: “What I will do is to urge Congress to restore the death penalty by hanging.”
He said permission to shoot to kill would be given for organised crime figures and people resisting arrest.
Mr Duterte courted controversy throughout his election campaign, threatening to kill drug dealers and dump them in Manila Bay.
He vowed to give himself and members of the security forces immunity from prosecution after leaving office, saying: “Pardon given to Rodrigo Duterte for the crime of multiple murder, signed Rodrigo Duterte.”
Last month a video emerged showing the candidate joking about a Australian woman who was raped and murdered in Davao while he was mayor, saying she was so beautiful “the mayor should have been first”.
In 2015, Human Rights Watch described Mr Duterte as the “death squad mayor” for his strong-arm tactics in Davao.
BBC