Interest in grants of up to $5000 to move away from Auckland has been "average".
The scheme started last Monday and is available to prospective social housing tenants, in an attempt to ease pressure on housing in the city.
Social Housing Minister Paula Bennett said officials had started interviewing people interested in the grants, but some had not turned up to interviews.
That was not unusual, she said.
"They have re-booked a lot of them, they have met some people and they're still working their way through it.
"I would call it average, a medium-level interest which is about right. It is a big move. It only started on Monday last week so it has only been just over a week."
Labour leader Andrew Little said the fact there wasn't a rush of people looking to take up the grant wasn't surprising.
"A lot of these people have work, they certainly have family and other connections in their community. It is a big deal, even with a $5000 cheque, to say, 'I'm going to up sticks and leave and restart a life somewhere else'.
"So it doesn't surprise me at all, I think it was a silly idea in the first place."
The size of the grant depends on how far people were travelling, the size of their family, and how many belongings they had.
An additional $2000 or $3000 could be paid to help people settle into their community.
They will not have to pay it back as long as they don't spend it on other things or return to the state house waiting list in Auckland within 12 months, except for exceptional circumstances.
The scheme, announced in January, was originally aimed at people on the social housing register.
It was extended to homeless people last month as the Government went into damage control over its handling of housing problems in New Zealand.