The National Party is accusing caretaker Prime Minister Chris Hipkins of playing politics over Gaza and says he did not consult them over calling for a ceasefire.
Hipkins says he sought an agreement from the National Party over the call but was unsuccessful.
National says it supports the goal, but says Hipkins' actions go against a long-standing bipartisan approach to foreign policy and Hipkins' statement that he had consulted National was "not entirely true".
Its foreign affairs spokesperson Gerry Brownlee told Morning Report that there had been talk on Friday about changing New Zealand's position on a ceasefire.
National had asked the Ministry of Foreign Affairs (MFAT) for advice leading to a reconsideration on its position, subject to certain conditions being met, such as the release of the Israeli hostages and a five-day ceasefire to allow humanitarian aid to reach Gaza. This would be aligning New Zealand's position with that of Australia and Canada.
"In the end this is an absolutely terrible situation and no one can look at the footage that you're seeing coming out of Gaza at the moment and not be deeply moved by the plight of the Palestinian people."
Brownlee said US diplomats were working with Qatari mediators to effect a ceasefire.
"Recognising that saying absolute things, like 'there must be a ceasefire' is not going to make it happen. It's something that you have to have a high degree of diplomacy around, unfortunately, and all through that, of course, Palestinian people and Israeli people are suffering.
"There has to be a whole process that goes in, and a lot of, frankly, forgiveness on both sides for us to get to a point where there would be a ceasefire, and I think recognising or stating what would be reasonable conditions for that to occur is quite a reasonable position.
"The whole situation is awful ... and it's very distressing to watch all that footage that we're seeing. But you have to recognise that there are very, very volatile parties to this and that there will be steps towards what we hope would be an end of the hostilities and an enduring peace."
National was not in favour of calling for an absolute ceasefire, "because there needs to be some degree of desire on both parties in the current conflict to go into that ... and both parties [to meet] a number of conditions."
Israel Institute co-director David Cumin was disappointed by Hipkins' call.
"When Hipkins was in government, he correctly called [Hamas] a terror organisation, and it's a little bit strange that he's now asking Israel to stop short of either eliminating the threat, and he's asking Hamas to be a part of the governing of a future Palestinian state," Cumin said.
Meanwhile, Pro-Palestinian supporters said it was "about time" Hipkins called for a ceasefire, and hoped National's Luxon would do the same.
Mina Al-Ansari was among a group of Pro-Palestine protesters who gathered in Auckland's Aotea Square on Sunday.
"This is the least they could do; this is the most humane act that we ask for," she said.
"We're really grateful for the thousands of people that have been turning up every single week [...] we really are trying to get our voices out there."
For another protester, Hanan Abulaila, a ceasefire could not come soon enough.
"All the world keeps watching, for nothing, why? Until when?"
Abulaila had family in Gaza. "They're moving from the North to the South. They bomb them, and 51 are killed."
Hipkins also called on Israel to allow the movement of supplies and for all parties to support people departing the conflict, as well as calling on Hamas to release the hostages without condition and be part of the process towards peace.
Greens urge unconditional calls for ceasefire
Green Party foreign affairs spokesperson Golriz Ghahraman told RNZ National and Labour were both playing politics and should be doing more.
"It's definitely progress - welcome on board Chippy, we've been here for a while - I'm not sure that the calls for ceasefire by either National or Labour has been as clear and unconditional as what we've seen from the Red Cross or UN Secretary General or other nations, so we're still looking for an improved, bold position from the big parties.
"We know that people of our nation want an immediate ceasefire and want our leaders to be working actively for peace ... they're both playing politics. They're trying to mimic what they see as their big trading partners and allies, they're not standing as New Zealand has stood before now when an atrocity happened, as a principled, leading voice for peace."
She said the calls for ceasefire should not depend on the release of hostages, just as the calls to release those hostages should not depend on whether Israel was willing to end the occupation of Palestine.
"That wouldn't have been acceptable because you cannot take civilian hostages, they have to be released immediately. The ceasefire must be immediate and unconditional - you don't get to bomb a civilian population in order to negotiate with a terror group.
"We definitely should and have - every party has - called for immediate unconditional release of hostages, but similar to that there needs to be an immediate unconditional ceasefire because we're seeing war crimes being committed, we've had experts say that this is now looking like genocide. It certainly looks like ethnic cleansing of the area."
Making the ceasefire demand conditional was a half-way solution that gave Israel a licence to continue violence against the people of Palestine, she said.
"You don't get to bomb two million people including a million children, you don't get to kill a child every 10 minutes, bomb hospitals where mums are giving birth to babies and people are getting cancer treatment, in order to negotiate with a terror group. It's just not lawful, it's not conscionable."
She said she welcomed the extra step Labour was taking but they and National should also be pressuring friends and trading partners to call for a ceasefire, call out the US government's funding of Israel's military, and lean on New Zealand's relationship with Britain.
Ghahraman will be hosting UN Special Rapporteur on the occupied Palestinian Territories Francesca Albanese to speak with MPs on Tuesday about the situation, and answer questions.
- with additional reporting by Finn Blackwell
Editorial note: Some of Gerry Brownlee's direct quotes that had been inaccurately transcribed have been amended.