However, the supermarket has a different version of events.
On Saturday afternoon, Mr Hawkins posted a photo to social media of himself with the flag unfurled outside New World Centre City.
He said along with his 8-year-old son he was considered an "intimidation risk" by staff there.
"I want to be clear", Mr Hawkins wrote.
"I have no time for activism that targets, harasses, or intimidates service workers.
"That’s not my style.
"But if that has happened, those instances can be dealt with as and when they arise.
"This level of blanket censorship — including of families just shopping for dinner — feels like a disproportionate response."
Yesterday, a Foodstuffs spokesman said the former mayor was not barred entry.
Instead, he walked off after staff asked him to leave his flag at customer services while he shopped.
He said the former mayor would be welcomed back and had not been barred from the store.
The store asked that shoppers leave flags outside or at customer services while in the store, the spokesman said.
"Following a rally in the nearby Octagon, a person was entering the store carrying a flag.
"One of our team members kindly requested that they leave the flag at customer services and the individual chose to leave instead.
"It’s important to note they were not barred from entering and they are welcome to return", the spokesman said.
Mr Hawkins’ posts garnered quite a lot of attention.
Among those expressing displeasure with the store was Dunedin city councillor Steve Walker, who said on Facebook he had now added the supermarket to his "boycott list".
A number of others expressed their disappointment in the supermarket.
"That’s absolutely disgusting behaviour", one commentator wrote.
Mr Hawkins yesterday said the reaction he received as he entered the store was "clearly" because of the particular flag he was carrying.
"We were initially told that we couldn’t come into the store because of the flag.
"When I asked why, the staff member just said they didn’t want to cause a scene.
"It was only when I asked for some justification that he said they’d had issues with their staff being intimidated."
Mr Hawkins said it was good to know he was welcome back, but it was still not clear to him what the issue was. He was prepared to give the supermarket the benefit of the doubt and accept the incident had been "handled clumsily".
Marching for peace in Palestine in Dunedin’s Octagon has been taking place every Saturday since the start of the war in October last year.
The United Nations Office for the Co-ordination of Humanitarian Affairs says since war broke out more than 41,000 Palestinians have been killed and about 95,000 have been injured.
About 1200 Israelis have been killed and 5400 injured as well.
The UN estimates 1.9 million people have been displaced in Gaza and about 70,000 homes have been destroyed.
