Greens foreign affairs spokeswoman Golriz Ghahraman tabled the motion in the House, asking MPs to recognise and support "the right of Palestine to self-determination and statehood, and recognise the State of Palestine among our community of nations".
It comes amid escalating conflict between Israel and Hamas, which governs the Palestinian territory of Gaza.
At least 200 Palestinians have been killed in the week of airstrikes, including 59 children and 35 women, with some 1300 people wounded, according to the Gaza Health Ministry.
Ten people in Israel, including a 5-year-old boy and a soldier, have been killed in the ongoing rocket attacks launched from civilian areas in Gaza towards civilian areas in Israel.
Ahead of question time today, Act, National and Labour all said they would not support it - it needed support of all MPs to be debated.
Ghahraman said the motion was designed to recognise the "harrowing violence" while looking forward towards lasting peace.
"The path forward from the latest bout of violence must be lasting peace, supported by the international community.
"Statehood as part of a two-state solution would uphold and celebrate the inherent rights and dignity of Palestinians."
Labour MP and Foreign Minister Nanaia Mahuta said today shortly before the House sat Labour declined to support the motion due to its wording.
They had tried to "reach agreement" but this did not happen, she said.
"We have been very consistent in our position around Israel and Palestine. We support self-determination and a two-state solution.
"Obviously for Palestine that would mean greater control around what happens in Palestine. We have asked for an immediate ceasefire so dialogue can begin."
Act foreign affairs spokeswoman Brooke Van Velden wrote to Ghahraman this week saying while they supported a two-state solution they would not support the Greens' motion, due to a "deeply concerning" tweet from Green MP Ricardo Menéndez March.
The tweet read "From the river to the sea, Palestine will be free!", which Van Velden said was a phrase used by Hamas, which she called a "terrorist organisation that calls for the elimination of Israel".
"We don't believe supporting the motion proposed by the Green Party is a helpful contribution to this discourse given the recent actions of Green MPs," she wrote.
National foreign affairs spokesperson Gerry Brownlee also said the party had long-supported the two-state solution to the decades-long conflict, but didn't feel this motion would be helpful.
"It is our position that the two sides need to desist from the current violent engagement and get back to the table on talks that could lead to this two-state solution that with commitment from both could bring peace to both states."
It was under a National government while New Zealand was on the United Nations Security Council that it sponsored a resolution against Israeli settlements as part of supporting a two-state solution.
Ghahraman said she was disappointed at the lack of support for her motion, saying it called into question support for the two-state solution.
"Supporting Palestine as a state puts pressure on the international community to do so as well, meaning the violence that triggered this would not have happened if Palestine had borders.
"I don't think they can continue saying they support a two-state solution if they do not support this.
"My motion is about looking forward to a future where children in Palestine and Israel can live in peace."
Regarding the tweet from Menéndez March, Ghahraman said she would not get "bogged down" into its meaning saying it had been used by many protesters including from Jewish communities here, but was "surprised" a politician would vote against something they believed in based on a tweet.
"I support freedom for Palestinians on equal terms as I support the freedom for Israelis to be safe in their homes.
"We have been hearing from Jewish and Palestinian communities, and all across New Zealand, with a longstanding kaupapa standing for peace, questioning why the Government has been so deafeningly quiet while these massacres are happening."
UN Secretary-General António Guterres has called the violence "utterly appalling" and, along with United States President Joe Biden, called for an immediate ceasefire.
However, despite three emergency meetings in a week the United Nations Security Council has come up with no resolution on the matter, according to Al Jazeera.
The parliamentary motion comes a week after Act put forward a motion asking MPs to declare a genocide was occurring against the Uighur Muslim minority in Xinjiang, China.
The Greens supported the motion, but it only succeeded after the term "genocide" was replaced with "severe human rights abuses".
