Bury Council's decision to refuse to fly the Israeli flag from the town hall on Yom Ha'atzmaut has angered the local community.
Karen Solomon, chair of the Yom Ha'atzmaut Committee, which organises communal celebrations in Greater Manchester for the day, said it was the first time the community had asked Bury to fly the flag, but the council has refused after a month of repeated requests.
A ceremony to raise the Pakistani flag on its independence day has run for some years at the town hall.
Ms Solomon said: "I quite innocently rang the council, after I heard about the Pakistani flag, to see if they would also fly one for Israel.
"We want to celebrate the Jewish people getting a state and share that with the whole community.
"But flying only one flag is not just insulting to the Jewish community, but also the Indian community, whose country's independence is celebrated on the same day as Pakistan's. They are offending other ethnic communities too. It's either all or nothing," she added.
Bury South MP Ivan Lewis said: "There will be significant anger within the Jewish community at this decision, and the apparent double standards which are being applied."
But Bury Council's leader, Bob Bibby, said the decision was not targeted at the Jewish community and that a review of its flag policy would be undertaken.
He said: "We have had so many requests, from the Polish, Irish, Italian and Indian communities. We already fly the Pakistani flag but that decision was not taken during my regime. This is getting a little bit beyond sense.
"There is no undercurrent to this decision, just that there are so many requests. I take on board what the Jewish community is saying. You can't make exceptions. That's why we feel a review of a policy is sensible and I've asked the chief executive to carry one out," he said.
But Mr Bibby said the review would not take place before local elections on May 5, making it unlikely that a decision on the Israeli flag would be made in time for Yom Ha'atzmaut on May 10.