The Palestinian federation (PFA) first proposed the sanctioning and suspension of the Israeli association in April
Fifa will carry out a legal assessment before it makes a decision on whether to agree to Palestine's call to suspend the Israeli federation over the war in Gaza.
The Palestinian federation (PFA) called for a vote to exclude Israel at Fifa's congress in Bangkok on Friday, which was supported in the room by the Jordanian FA.
Fifa president Gianni Infantino said it was a matter for the Fifa Council to make a decision on, following a legal assessment.
"How much more must the Palestine football family suffer for Fifa to act with the same severity and urgency as it did in other cases?" PFA president Jibril Rajoub said.
"Does Fifa consider some wars to be more important than others and some victims to be more significant?
"I ask you to stand on the right side of history. The suffering of millions, including thousands of footballers, deserves as much. If not now, then when? Mr President, the ball is in your court."
The war in Gaza began after a 7 October Hamas attack on Israel, which killed about 1,200 people. More than 252 others were taken hostage.
More than 34,000 people have since been killed by Israel's offensive in Gaza, the territory's Hamas-run health ministry says.
Shino Moshe Zuares, the president of the Israel Football Association, said: "We are facing a cynical political and hostile attempt by the Palestinian association to harm Israeli football.
"Seven months after the terrible day, when football matches cannot be played in large parts of Israel, north and south, and over 130 Israelis are still being held in Gaza, it is injustice that even in these circumstances we find ourselves fighting for our basic right to be part of the game."
Infantino said a legal assessment of the allegations made by the PFA would be undertaken urgently, with the Fifa Council convening an extraordinary congress in late July to address the issue.
"Football should not and should never become a hostage for politics and always remain a vector for peace, a source of hope, a force of good, uniting people rather than dividing," Infantino said.
"This legal assessment will have to allow for inputs and claims of both member associations. The results of this analysis and the recommendations which will follow from this analysis will subsequently be forwarded to the Fifa Council."
A new, expanded 32-team men's Club World Cup is to be held in the United States next summer
Infantino has played down the prospect of legal threats over plans for a 32-team men's Club World Cup next summer.
The world governing body faces a legal threat from players' union Fifpro and the World Leagues Association if it continues with plans to host the tournament.
Earlier this month, Fifpro and the WLA said the global football calendar is "beyond saturation" and that "players are being pushed beyond their limits".
Speaking at Fifa's 74th congress Infantino said he hoped Fifpro and the WLA should stop this "futile debate".
"Even with the new Club World Cup of Fifa with 32 teams and 63 matches every four years, Fifa is organising around 1% of the games of the top clubs in the world," he said.
"All other matches, 98, 99%, are organised by the different leagues, associations, confederations, by all of you, – and that's good.
"But here comes the thing – the one or two per cent of matches that Fifa organises is financing football all over the world."
Manchester City and Chelsea are among the 12 European representatives at the expanded Club World Cup, to be held in the USA between 13 June and 15 July 2025.
"The revenues that we generate are not just going to a few clubs in one country. The revenues that we generate are going to 211 countries all over the world.
"There is no other organisation that does that. So I hope these figures – which you can of course check and calculate – should probably stop this futile debate which is really pointless."
Infantino said 70% of Fifa's member associations "would have no football" without without the governing body's resources.
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