Police investigations are ongoing although local media report the prime suspect, a prisoner out on parole, is in police custody.
The call from the victim's parents and immediate family has stirred up public debate about penalties for serious criminal offences in the country.
The Chairman of the Vanuatu Christian Council Allen Nafuki said he would be convening a meeting of the council this week to discuss the issue but said he personally felt there was no place for capital punishment in Vanuatu.
"Like in the Christian perspective and also Kastom perspective we are not allowed. We are saying no, no to capital punishment. So this will be picked up by the government but as far as I understand people are not in favour, even the chiefs of these islands and our custom leaders do not recognise that," said Pastor Nafuki.
But the chief executive of the Vanuatu National Council of Women, Leias Cullwick, said she supports the family's call for capital punishment to be introduced saying serious deterrents are long overdue.
"The country needs to have a death penalty because now the issue sort of happen recently with very innocent young children. It is just not acceptable. We have discussed these issues as well and being a Christian country it doesn’t give you a right to go killing anybody so we need to have a deterrent in place to make sure that people's lives and their livelihoods is respected," said Leias Cullwick.
However the chairperson of Vanuatu Women Against Crime and Corruption Jenny Ligo says she feels what is needed is stricter enforcement of the existing laws.
"The parents their child is dead so they have a right to make that call and it is upon the decision makers now to do what they feel is better for Vanuatu. I think women of Vanuatu we would like our lawmakers to do the right thing. They have to make sure that our laws are enforced to make sure that Vanuatu is safe," Jenny Ligo said.
As investigations continue the Vanuatu Daily Post reports the prime suspect is being kept in police custody to protect him from the victim's angry relatives.