Each family will have a member of that team as their personal contact.
The men have been trapped underground in the mine near Greymouth for about 40 hours and fears for their safety are increasing.
Mr Whittall told media this morning it was still not safe for rescuers to enter the mine due to dangerous levels of toxic gas.
A new hole with a diameter of 15cm will be drilled today to be used to take further air samples nearer to where the men were thought to be trapped, but this would probably take about 16 to 24 hours to complete.
As well as gas samples being taken, if the hole was big enough devices such as a camera could be dropped into the mine, Mr Whittall said.
The rig will drill 150m-200m into the mountain.
"We've got a location for that and that will be a couple of hundred metres further into the mine from where the shaft is and that will give us slightly different information and will give us information with what's going on," Mr Whittall said.
The drill will tunnel through hard rock and Mr Whittall said it could take longer than 24 hours to complete.
Tasman District police area commander Superintendent Gary Knowles said he was not prepared to put rescue teams underground while there was a risk to their safety.
"The teams are active, the rescue crews have been practising all night and they'll be changing this morning - so they're sitting there this morning training ... and looking at the risk options so when that window of opportunity opens, we're going underground.
"We're still focussing on a rescue operation. I would like to get underground and bring these guys out."
It was not a case of putting a gas mask on and attempting to recover the men as the risk was too big, Mr Knowles said.
"We're not going to put 16 guys underground to effect a half-arsed rescue."
International experts from Australia and other countries had arrived overnight.
Twenty-four New Zealanders, two Australians, two Britons and one South African have been out of contact with mine management since an explosion about 4pm on Friday.
Two men, who were working alone escaped the mine, Russell Smith, 50, and Daniel Rockhouse, 24.
They suffered moderate injuries but have now been discharged from Grey Base Hospital.
Greymouth mayor Tony Kokshoorn has called for the names of the 29 trapped miners to be made public.
Police are yet to officially release the names of the miners, a stance that has been criticised by Mr Kokshoorn.
"I'm all for disclosure of the names to avoid speculation. Everyone knows locally - it's not a secret and anyone could find out if they wanted to," he said.
"Everyday we don't hear a voice from down there we get more desperate. We are between a rock and a hard place and we don't know what's wrong.
"I don't see the point in keeping it (the names) secret."
He said he could see the despair on the faces of the men's relatives.
"Everyday is crucial, it's like a clock that's ticking down."
Police have defended their decision not to release the men's names until all the families of the workers - especially those from overseas - had been informed of the situation.
Prime Minister John Key promised the miners' families the Government would give them every possible support and that everything possible would be done to rescue "the 29 brave men".
View Pike River coal mine in a larger map
- NZPA
