National will block attempts by Opposition parties this week to introduce bills that could have seen New Zealand immediately take more refugees.
Labour and the Greens will both seek leave from Parliament to introduce their bills they hoped could have brought more refugees into the country.
Millions of people are fleeing war zones in the Middle East and Africa with many seeking shelter in the European Union, and over the past week, the calls for New Zealand to take some of those refugees have grown louder.
Prime Minister John Key said the Government was still considering all its options, but he was not ruling out doing more.
"But we need to take advice on that to ensure any decisions made can be backed up with the same level of support and assurances we give to other refugees that come to New Zealand," a spokesperson for Mr Key said.
In the meantime, the spokesperson said, the National Party would not support the proposed legislation from opposition parties.
On Tuesday, Labour leader Andrew Little will attempt to introduce an Emergency Humanitarian Response Bill that would lift the quota by an extra 750 refugees.
Mr Little said there was a humanitarian crisis unfolding on the other side of the world and New Zealanders were crying out for the Government to do more.
"The failure to do anything so far is I think distressing a lot of New Zealanders.
"If next week, we don't see any change on the Government's part, as well as obstructing moves by ourselves and the Greens to try to do something then I think New Zealanders are going to be extremely disappointed," Mr Little said.
The Green Party will also try to fast track the bill in the name of its immigration spokesperson Denise Roche which would increase the quota from 750 to 1000.
Ms Roche said the bill reflected the public's desire to help. "We know that New Zealanders are fair minded, we know that they are compassionate," said Ms Roche. "And we know that there are more and more of us who want to open our borders and open our homes to give people a safe haven."
New Zealand First leader Winston Peters said New Zealand was known for its strong humanitarian principles.
He said he could not understand Mr Key's inaction nor the fact he was casting aside other ideas.
"I think across the whole political divide people would be prepared to do something in this case, as long as we had a proper check on these people who are coming."
United Future leader and Government support partner Peter Dunne said he would have supported the bills because something needed to be done sooner rather than later.
"It's fair to say that both bills were political stunts but I would have supported them because I think that the sentiments that they contain are where most New Zealanders want to see this issue head.
"Most New Zealanders who have expressed views to me over the last few days are strongly in favour of both looking again at the size of the quota and some sort of emergency package," Mr Dunne said.
Maori Party co-leader Te Ururoa Flavell said his party would have also supported the opposition bills to boost the quota.
He said he was happy to hear Mr Key had sought more information on what could be done, but something needed to be done quickly.
"The hope would be that we don't have to wait too long... because certainly the crisis is getting bigger as the days go by, so certainly we've got to do something pretty quickly," Mr Flavell said.
ACT's David Seymour said he would not have objected to the Greens bill but he felt Labour's was poorly thought through.
The National Party's youth wing, the Young Nats, called on the party to bring forward its refugee quota review planned for next year.
In an open letter to MPs, the Young Nats said the majority of its supporters believed New Zealand could and should be doing more.