He added that he would also seek to give security forces shoot-to-kill powers for suspects who evade arrest and those involved in organised crime.
It is unclear how easily he could enact such proposals, but analysts credit his success to his tough stance on crime.
He is set to be sworn into office on 30 June for a term of six years.
While official election results have not yet been announced, Mr Duterte has an unassailable lead. He will need the backing of Congress to see through his plans.
Speaking at a press conference on Sunday in the southern city of Davao, Mr Duterte is also quoted as saying that he wanted to forge closer relations with China, and that he was open to direct talks over territorial disputes in the South China Sea.
The Philippines has taken one of its claims to a court of arbitration at the Hague.
Controversial record
Mr Duterte's record as the crime-crushing mayor of the southern city of Davao, once notorious for its lawlessness, has earned him the moniker The Punisher.
"What I will do is urge Congress to restore death penalty by hanging," Mr Duterte told reporters The Philippines abolished capital punishment in 2006.
Duterte: From 'Punisher' to president
- Born in 1945 into a political family but with a more modest background than many Philippine politicians
- Married twice but now single, he says he has several girlfriends
- A lawyer, he became vice-mayor of Davao in 1986 and mayor in 1988. He has also previously held a seat in congress
- Built a reputation fighting crime, militancy and corruption. He has promised to continue his tough stance as president, but has offered few specific policies
- Well known for incendiary comments, such as saying he would kill thousands of criminals without trial
"If you resist, show violent resistance, my order to police (will be) to shoot to kill. Shoot to kill for organised crime. You heard that? Shoot to kill for every organised crime," he is quoted by the AFP news agency as saying.
Rights groups say hundreds of criminals were killed by so-called "death squads" in Davao during Mr Duterte's stewardship of the city. In 2015, Human Rights Watchdescribed Mr Duterte as the "death squad mayor" for his strong-arm tactics in Davao.
Whether Mr Duterte is able to persuade Congress to back such policies remains to be seen.
Last week his spokesman put forward a series of proposals such as a ban on alcohol in public places and a "nationwide curfew" for children.
Mr Duterte was not afraid of courting controversy throughout his election campaign. 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."
Duterte in quotes
On vowing to kill criminals
"Forget the laws on human rights... You drug pushers, hold-up men and do-nothings, you better go out. Because I'd kill you. I'll dump all of you into Manila Bay, and fatten all the fish there."
On the rape of a female missionary
"I saw her face and I thought, son of a bitch. what a pity... I was mad she was raped but she was so beautiful. I thought, the mayor should have been first."
On the Pope's visit holding up traffic
"We were affected by the traffic. It took us five hours... I wanted to call him: 'Pope, son of a whore, go home. Do not visit us again'."
On taking Viagra
"I was separated from my wife. I'm not impotent. What am I supposed to do? Let this hang forever? When I take Viagra, it stands up."