Prime Minister John Key says he would prefer not to increase New Zealand's annual quota of 750 refugees.
There have been calls from Amnesty International for an increase in refugee numbers to reflect the higher number of asylum seekers internationally.
But Mr Key said he thought it was more important to settle those who came to New Zealand well than to increase the overall quota.
"The issue here is, if we take more will we do as good a job?"
Mr Key said he accepted the issue of taking refugees was an international problem.
"New Zealand participates in all of those [refugee] conferences, we put in money and aid.
"But if you look at the scale of the issue - because it is a very significant issue - if we were to go back to our original target and go up from 750 to 850, or go from 750 to 1000, it's hard to believe that's going to resolve the issue because we're talking about millions of people."
Mr Key said information that a boat of refugees found off the coast of Australia was bound for New Zealand was credible and accurate, but could not confirm where the information had come from.
"Two weeks ago the official advice came from - not just New Zealand - was highly informed."
Amnesty International's global Secretary-General Salil Shetty said New Zealand needed to show leadership around taking refugees when it takes on the presidency of the UN Security Council in July.
Mr Shetty said New Zealand was 87th in the world in terms of per capita refugee protection numbers, and that the number had not changed for 30 years.
He said the organisation was asking for New Zealand to double its annual quota of refugees to 1500.
"Prime Minister Key is right, it's not going to change everything ... but even doubling it would be an important signal to the world."
He said that the issue of boat people should be addressed by the Government.
"We really have a problem which is much closer [to] home now.
"One of the big mistakes that the European countries did I think was to wait for all the drownings to happen - thousands of people to lose their lives in the Mediterranean - I don't think New Zealand should wait for that to happen.
"People are fleeing from persecution from crisis - people are already on the boats so I think there's no real choice but to address that issue as well."
Mr Shetty said he planned to try and to convince Mr Key to double the numbers when they meet later today.
Call to help refugees from Myanmar
A refugee who fled the military government in Myanmar has described how coming to New Zealand has saved her life and her children.
Sue Leya has added her voice to those calling for the Government to increase the quota of refugees it takes.
She arrived here in 2007 with two young children on a UN agency refugee programme.
She now works at a Nelson primary school helping refugee children with language skills and is grateful to be here.
"So lucky to come here - New Zealand - and it's very peaceful compared to [my] past life ... I'm so grateful to be here."
She said there were many more families needing help.
Thousands of migrants, mostly Bangladeshi or Rohingya Muslims from Myanmar, have also arrived in Indonesia, Malaysia and Thailand since the beginning of May.
The Refugee Council also called on the Government to take emergency action to alleviate the refugee crisis.
The council's vice-president Colin Henry said if New Zealand accepted more refugees from Myanmar, other countries may follow.
Mr Henry said the UN Refugee Agency has been asking countries to accept more refugees in emergency situations.