The agency said it had received nearly 7400 applications lodged under the previous parent category and under the now defunct adult child and sibling category.
Under the new scheme introduced this month, tier-one applicants on higher incomes are given priority over poorer migrants who speak little or no English.
To qualify for the top tier and cut processing time to 18 months, sponsors must have an annual income of at least $65,000 or bring at least $500,000 s to New Zealand.
Two hundred and thirty applications under the new policy have been lodged under tier one and 16 under tier two.
Nearly half the tier-one applicants are from China, quarter from Britain and the rest from various other countries including South Africa, India and Russia.
China nationals account for 12 of the 16 applications lodged under tier two.
Mr Stevens said applications lodged under the previous parent category would be processed after tier one, and tier two would be looked into only after these were cleared.
Chinese immigrant Kathy Lin, whose husband had an application lodged under the previous category to sponsor his parents, said a five- to seven-year wait was "unfair and ridiculous".
"My in-laws are in their 70s and they may not be around in seven years," she said. "The reason we want to sponsor them here is because we want to spend time with them in the final years."
Mrs Lin, an accounts assistant, had received an email from Immigration asking her to pay $420 for an expression of interest to take her application to tier one, but said she could not meet the requirement as she was working part-time.
"It is unfair because if my in-laws were here to help look after my two children, I could work fulltime and easily meet the tier-one financial requirements," she said.
The number of people granted residence through the parent category is limited to about 4000 annually.
LONG WAIT
Parent sponsorship waiting times
* 7 years: Applicants who do not meet minimum wealth levels.
* 5 years: Applications lodged under the old parent category.
* 18 months: Applications lodged by rich migrants.
Source: Immigration New Zealand