Women who get pregnant while in New Zealand on temporary residency permits are being told to leave the country to have their babies because of a shortage of maternity services.

The women are being told they cannot give birth here even if they are prepared to pay the full medical and maternity care costs.

Immigration New Zealand has told one pregnant woman that - despite her financial stability - she would "be putting an additional strain on our already short services", which the department claimed were "stretched in most areas of the country".

Two married international students - facing removal orders after becoming pregnant - say the decision to throw them out is "unduly harsh and discriminatory".

One said she planned to complain to the Human Rights Commission. But a commission spokesman said that although the Human Rights Act listed "discrimination due to pregnancy", there was specific provision to exempt immigration matters.

One of the aggrieved students, a 29-year-old from China who is six months pregnant, said Kiwis criticised her country over its lack of human rights, but international students who became pregnant in NZ had fewer rights than anyone in China.

She is appealing against her removal order and does not want to be named for fear that her speaking out might jeopardise her appeal.

"My mother keeps phoning me to say it is no good to cry while I'm pregnant," she said, "but I am crying every day because I don't know what else I can do."

Sung Won Kim, 31, a horticulture student at the International College of Auckland, said she was "at a loss" after being told she had to leave New Zealand by June 21, because, she says, her pregnancy means she will not be eligible for a further permit.

"My husband is in New Zealand and runs a business in New Lynn. We have been paying for all our medical care and proven that we have more than $38,000 in our bank account.

"We are prepared to pay the costs up front. We're not expecting anything free or to receive any special treatment in New Zealand, so how can they do this to me and my baby?"

In the past, some foreigners wanted their children born in New Zealand to obtain citizenship, but the New Zealand Citizenship Act was changed in 2006 to require at least one of the parents to be a New Zealand citizen for this to happen.

In a letter supporting Ms Kim's appeal, college principal James Zhu wrote: "We understand pregnancy is an ordinary event in everyone's life ... Refusal of the student permit will cause extreme stress, which will be hard on a pregnant woman and which seems not necessary."

The Ministry of Health estimates the average cost of an uncomplicated pregnancy and delivery to be about $4000, but the amount can reach $8500 if there are complications.

The Department of Labour, which oversees immigration, says paying maternity costs up front will not make any difference to an application because pregnant women will be deemed to be "not of an acceptable standard of health".

"This is because of the costs and scarce resources in the maternity sector, and the applicant offering to fund her own maternity costs does not cover the demand for services," a department spokesman said.

"There may also be a question of whether the person is able to undertake the course of study on the basis of which they are applying for a visa or permit if pregnant."

Exceptions were granted for partners of NZ citizens or residents and, in some cases, to people applying for a work-to-residence visa or permit.

He said women on temporary permits were also obliged to inform Immigration if they became pregnant.

"If a person's circumstances have materially changed since they obtained a permit, they are obliged under the Immigration Act to advise us of that change.

"Becoming pregnant is a material change. Failing to inform INZ of this could mean the person is in breach of the conditions of their permit."

The department said it did not have information on how many temporary visas had been declined due to a woman being pregnant.