The Palestinian flag has been raised outside Bradford City Hall to recognise the "suffering and deaths of hundreds of people in Gaza", the council said.
More than 1,000 Palestinians and 39 Israelis have died since the Israel-Hamas conflict began on 8 July.
Labour leader of Bradford Council, David Green, said the authority was not "taking sides" in the conflict.
But David Israel of the Leeds Jewish community said the council should raise the Israeli flag as well.
'Clearly taking sides'
Mr Green told BBC Radio Leeds: "The flag is not being raised in support of one side of the conflict, i.e. Hamas or the Israeli army.
"The flag is being flown in recognition of the suffering and deaths of hundreds of people in Gaza.
"Bradford has a long history of supporting innocent civilians who are suffering through war and conflict and this is just another example of the concern that has been raised by citizens in Bradford of all faiths and none, about the suffering happening to innocent Palestinians."
But Mr Israel said the council was "obviously and very clearly taking sides in the conflict".
"I'm sure David is also aware that innocent Israeli civilians have suffered through war and conflict," he said.
"If you're going to put up one flag you need to put up the other flag to show support for innocent civilians on both sides on the conflict."
Last week Bradford East Liberal Democrat MP David Ward apologised for comments he made about the conflict on Twitter.
Mr Ward tweeted on Tuesday: "The big question is - if I lived in #Gaza would I fire a rocket? - probably yes."
In a statement later released by the Lib Dems, he said: "My comments were not in support of firing rockets into Israel. If they gave the opposite impression, I apologise."