Central to the law and order push is reviving the death penalty, which is currently in place for treason, piracy and wilful murder but has not been used since 1954.
"Among the methods discussed include death by firing squad, considered more humane and inexpensive than other methods like lethal injection and electrocution," the Post-Courier newspaper said, citing a government statement.
A final decision on the method has yet to be made but the plan is to build an execution centre at a new maximum security prison on a remote island, the newspaper added.
The proposed laws follow a spate of horrific crimes against women including a beheading and the burning alive of a mother accused of witchcraft, as well as the gang rape of two foreigners last month.
"The level of these serious crimes in our community, particularly crimes of sexual nature and murder are unacceptable," said O'Neil.
"The heinous behaviour is perpetrated by a few, but the country at large is made to suffer. We must act now to protect the majority.
"The proposed laws are tough, but they are necessary. We have to address a situation that is destroying our country."
The church voiced strong opposition to the death penalty, preferring life imprisonment with hard labour for murder and rape.
Catholic Archbishop of Port Moresby John Ribat acknowledged the government must act, but said death was not the answer.
"No life will be taken. We do not have the right to do that but we do have the right to better a person's life," he said.
Under the proposed legislation, PNG would also repeal its controversial Sorcery Act, meaning any black magic killing would be treated as murder, a move international human rights groups and the United Nations have lobbied for.
Though it criminalises the practice of sorcery – in which there is a widespread belief in PNG – the 1974 act has been criticised.
Human rights groups said it led to an increase in false accusations and gave the notion of sorcery a legitimacy it would not otherwise have had.
All rapes would attract a penalty of life in prison without parole, with a new maximum 20-year jail term for making home-brew liquor.
Marijuana and other drug cultivation would be punishable by 50 years in prison, while armed robbers would face 30 years' jail. [Telegraph]