Israel had murdered more than 11,000 Palestinians, including 5000 children, in the war against Hamas, Cr Marie Laufiso said.
She also referred to United States President Joe Biden as "Genocide Joe".
The Holocaust Centre of New Zealand labelled her comments inflammatory and belittling.
A simplistic "goodies and baddies" narrative did nothing to advance peace for Palestinians and Israelis "but inflames an environment in New Zealand where there has been escalating and highly concerning antisemitism", centre chairwoman Deborah Hart said.
"It is irresponsible, particularly for leaders charged with civic responsibilities in their region."
In a notice of motion for next week’s Dunedin City Council meeting, Cr Laufiso asked for the Palestinian flag to be flown on November 29, which is the United Nations international day of solidarity with the Palestinian people.
This would be "a tangible and visible symbol of support to our local Palestinian community", Cr Laufiso said in the notice, supported by Cr Steve Walker.
The notice calls for the council to agree to flying the flag from the mayor’s balcony in the Civic Centre and other city buildings.
It also asks the council to follow the lead of Christchurch Mayor Phil Mauger in his Armistice Day letter to the Mayors for Peace, calling for an immediate ceasefire in Gaza.
The war between Israel and Hamas has been running for almost seven weeks.
A four-day truce was announced this week to provide a humanitarian pause and facilitate the freeing of 50 hostages taken by Hamas in exchange for about 150 Palestinians in Israeli prisons.
However, Israeli prime minister Benjamin Netanyahu has said hostilities will resume after the temporary ceasefire and war will continue until Hamas is eliminated.
The timing of the truce appeared to be not quite settled yesterday.
Cr Walker said a humanitarian crisis of the highest order was unfolding in Gaza.
"With the ongoing indiscriminate killing of innocent women, children, elderly and other innocents with zero connection to Hamas terrorists, there is no more appropriate time for council to take a stance," he said.
The conflict began on October 7, when Hamas launched attacks from Gaza into southern Israel, killing at least 1200 people, mostly civilians. Hamas fighters took 240 people hostage and killed hundreds at a music festival.
More than 13,000 civilians have since been killed in Gaza, including thousands of children, the UN believes.
Cr Walker said he supported nations having a right to self-defence and he, "along with the vast majority of those calling for a permanent ceasefire, absolutely condemn the actions of Hamas and call for the release of all hostages taken on October 7".
"Flying the Palestinian flag on the international day of solidarity simply provides an opportunity for our community to focus its attention on the fact that the question of Palestine remains unresolved and that the Palestinian people have yet to attain their inalienable rights," Cr Walker said.
Those were "the right to self-determination without external interference; the right to national independence and sovereignty; and the right to return to their homes and property, from which they have been displaced".
Cr Laufiso characterised the conflict as being between a powerful nation and an oppressed people and she added "since 1948, Palestinians should not have been paying the price of the Third Reich’s Holocaust".
Asked if flying the Palestinian flag might be inflammatory and distract from what happened on October 7, Cr Laufiso said she found Israel’s actions to be inflammatory.
"Because of October 7 (never mind the decades, months and days leading up to that day), Israel is somehow perceived as a victim of Hamas.
"I personally find it intriguing that a high-tech, sophisticated intelligence army such as the [Israeli Defence Force] was ‘surprised’ by a low-tech (motorbikes and para-gliders) attack launched by Hamas."
Ms Hart noted Cr Laufiso did not mention the Israeli hostages.
The Holocaust Centre advised terms such as "genocide" should be used appropriately and Ms Hart said the centre stood with compassion "for all innocent people adversely affected by the recent conflict in Israel and Gaza".
"It is a time for leaders to take great care with their language and deeds to ensure they do not exacerbate an already inflamed situation for Jewish people."