They have decided instead to lower the New Zealand flag to half mast, in recognition of suffering on both sides of the conflict in Gaza.
They also endorsed Christchurch Mayor Phil Mauger's call for a ceasefire between Israel and Hamas.
The vote in each case was 12-2 and the two councillors against were Lee Vandervis and Bill Acklin.
Both had been wary of the Dunedin City Council getting involved in matters they said were not core council business.
November 29 is the United Nations international day of solidarity with the Palestinian people and it falls this year after about seven weeks of war that have devastated Gaza.
The latest conflict started on October 7, when Hamas fighters killed about 1200 people in Israel, mostly civilians. Israel responded with air and ground assaults in Gaza and concern has mounted about a particularly high death toll for women and children.
A temporary truce holds at the moment.
The compromise of flying the flag at half mast was suggested by Cr Andrew Whiley, who credited his wife with the idea.
Councillors said they had received more than 100 emails about the war and the proposal of flying the Palestinian flag and calling for a ceasefire.
Many of them expressed deep pain and emotion, they said.
Seven of eight speakers at this morning's public forum talked about the Palestine issue.
They came from both sides of the fraught subject.
The meeting began with Dunedin Anglican dean Rev Tony Curtis reading a passage of scripture and saying a prayer.
"Today will be a day of high emotion," he said.
"This day will be hard for many of us, but harder for the people of Gaza and Israel who have lost whanau to violence and hate."
He cautioned against people being demonised and dehumanised.
"It is only by lifting each other up that we will find peace."
Yana Greenman, a granddaughter of Holocaust survivors, said the initial proposal put forward by Crs Laufiso and Walker was deeply concerning, as it was provocative and one-sided.
Rula Abu-Safieh supported the original motion and it was later understood she was comfortable with the compromise.
She spoke of 75 years of what she described as cruel military occupation by Israel.
Dr Abu-Safieh noted hundreds of people had demonstrated peacefully in Dunedin in support of Palestine for seven consecutive weeks.
Nigel Woodley said a permanent ceasefire would be premature while Hamas was still in power in Gaza and when not all hostages had been released.
James Irwin said Jewish people were homeless for centuries and they were targeted by pogroms and persecution.
Flying the Palestinian flag from civic buildings would not assist social cohesion, he said.
Chris Caradus told the council "peacemakers do not take sides".
Crs Laufiso and Walker accepted the compromise put forward by Cr Whiley, and Cr Laufiso said she did so because Dr Abu-Safieh was comfortable with it.
Cr Walker said showing solidarity with Palestinians did not amount to endorsement of Hamas militants.
Empathy with Palestinians did not mean sympathy for Hamas.
"This is not about taking sides," he said.
It was about standing up for children and opposing needless loss of life, he said.
The death toll in Gaza was 14,000 and rising, he said.
Cr Laufiso said a new phrase had been coined in the past seven weeks - WCNSF, or wounded child and no surviving family.
"We want the murder of children to stop," Cr Laufiso said.
"Eight-thousand children have been killed."
She objected to what she called a "colonialist, genocidal project" that had gone on for decades.
Cr Whiley said feedback he had received from both sides was raw.
He acknowledged the pain and suffering.
"I do not believe it is the council's role to favour one group of residents over another."
Cr Carmen Houlahan said the situation in Israel and Gaza was highly inflamed, the original motion was divisive and she was wary of "telling other countries how to do their wars"
Cr Christine Garey said the motion had enabled a fruitful discussion to happen at the council meeting.
She had a question for people who viewed the issue as not relevant to local government: Where is your humanity?
"Our support is for the Palestinian people, not Hamas."
Cr Jim O'Malley called for a proper investigation into war crimes from both sides.
There had been a cycle of violence and revenge.
"This is a region of tragedy," he said.
Retribution and revenge had been allowed to stand above forgiveness, he said.
In her closing speech, Cr Laufiso talked about the struggle to end apartheid in South Africa.
"Collective efforts over decades ended apartheid in South Africa," she said.
"A similar approach must happen for Israel."