The Government is talking to the police about whether the names of those listed as missing in Christchurch could be made public.
As of Tuesday morning, nearly a week since the earthquake, 154 people are confirmed dead and about 50 are listed as missing.
Prime Minister John Key says talks were held on Monday about resolving the names issue.
He says it can be farcical when families are talking to media about the loss of their loved ones but they cannot be named yet.
The chief executive of Victim Support, Tony Paine, says the families are frustrated but there's nothing anyone can do.
He says about 50 Victim Support volunteers are working with the grieving families in conjunction with specially trained police.
Mr Key says the police are doing the best they can in a very challenging situation.