Prime Minister Jacinda Ardern says some victims' bodies will be returned to families on Sunday and it's hoped all will be returned by Wednesday.
On Sunday afternoon, Ardern said a "small number" of bodies, currently in the Christchurch Hospital morgue, would be returned by that evening.
Affected families are eligible for funeral grants of about $10,000 through ACC. There would be leniency given for victims and families who are not New Zealand citizens.
Police have 90 disaster victim identification officers, including 20 from overseas, working to identify the victims and return them to their families.
Chief Coroner Judge Deborah Marshall, two other coroners and four support staff are in Christchurch to support two local coroners and help speed up the victim identification process.
Marshall said coroners, police and forensic pathologists were working as quickly as they could to establish the identities of those who lost their lives.
She said they were following a process that met international best guidelines.
"There could be nothing worse than giving the wrong body to the wrong family, and we find from overseas examples that when you try to speed up the process or miss out steps, that is exactly what happens, and its not going to happen here."
The process involved the bodies and personal items on them being examined in detail. Police separately gather information on those who are missing such as physical descriptions of them and their clothing, medical records, and fingerprints from official records.
This information is then matched up, with coroners making the final decision on whether they are satisfied the identity has been confirmed.
"This is a process we have to go through and we will be going through it with every single body," Marshall said.
She said identification hearings would start on Sunday afternoon and it was expected the process of returning the deceased would begin that night.
Christchurch mayor Lianne Dalziel said police and coronial services are working "as hard as they could" to get victims' bodies returned as soon as possible.
"There's an [Islamic] cultural imperative about burying the bodies within 24 hours," Dalziel said. "I've talked to some of the community leaders and they're now satisfied and there's agreement about how quickly that can happen, after coronial work is complete."
Sextons from out of town have travelled to Christchurch to help prepare graves in the city's eastern suburbs, she said. "The burial sites are really important. The graves have to be facing the right way, and they have to be a particular size. There's a lot of work to do and things have to be ordered in."
It is not clear when funerals will begin.
Police Deputy Commissioner Wally Haumaha said police understood that the families not being able to bury their loved ones quickly, according to their religious duty, was an added trauma for them.
"Our sole focus is to get their loved ones back and to follow the cultural traditions such as the washing and shrouding of the loved ones, and we have made premises available to carry out these sensitive cultural issues"
He said authorities were working closely with Imams from local and national mosques and the Federation of Islamic Associations of New Zealand. He would not say when it was hoped all bodies would be released to the families.
Muslim volunteers have also been arriving from across the Tasman to help with the custom of washing the bodies.
Ali Armando flew in with a group from Brisbane, reporting to the makeshift crisis centre at Hagley College after Friday's deadly mosque terror attack in Christchurch.
Volunteers are offering support for the families of the terror attack victims, security around the area and ghusl – the Islamic practice of washing the dead.
"We're ready so that as soon as they start releasing the bodies, we'll do the washing," Armando said.
Armando said as soon as he received news of the terror attacks, he knew he needed to come to Christchurch.
"I'm going to jump on a plane and come and do whatever I can as a human being, as well as a Muslim," he said.
"The [alleged gunman] was an Australian himself, so as Australians we feel like we should do whatever we can do to help."
He said moral support was important and Islamic protocols needed to be followed, with families having to refrain from weeping or wailing.
"We believe the soul can still hear or understand what's happening around it, so we just be quiet, respect the body and do what needs to be done."
'CHANCE TO HELP OUR BROTHERS'
Armed police were still standing guard on the street outside the college as the volunteers arrived.
Tazrul Islam said he had also flown in from Auckland to help with ghusl.
"First the body needs to be washed and a prayer said over it before it can be buried," the 23-year-old said.
"This is our chance to help our brothers."
Another man, heading into the college, said he had just flown in from Australia.
"One of my Fijian mates got shot, so we're here supporting him."
The college is also being used as a place for the Muslim community to gather together.