The Palestine Football Association (PFA) argued that the presence of six Israeli football clubs playing inside settlements, that are seen as illegal under international law, are also in breach of FIFA statutes.
PFA President Jibril Rajoub called for the FIFA Congress "to stop all football and football related activity run by the Israeli federation in Palestine's internationally recognised territories".
"We're not looking for an expulsion [of Israel from FIFA]," Rajoub said at the Congress.
"We want to stop all football and football-related activity run by the Israeli federation in Palestine's internationally recognised territories."
However, in the Bahraini capital Manama on Thursday, the FIFA Congress voted 138-50 in favour of the matter being postponed until October, a motion presented by FIFA President Gianni Infantino following presentations by the chiefs of the Palestine and Israel football federations.
"We will take responsibility and we will take a decision on this matter," said Infantino.
Rajoub also accused Israel's prime minister of "interference" in the matter by making a "phone call to the FIFA president demanding the proposal to be removed from the Congress agenda".
"Football cannot be played without respecting human rights. Such an interference [Netanyahu's alleged phone call] affected us all, that's something nobody has done before."
Last month, the PFA had accused Israel of using backdoor diplomacy to block Palestinian calls for sanctions.
The PFA called the Congress' postponement vote illegal and vowed not to wait until October before taking action against the decision.
"While it's too early to decide an option, the main thing to note is that what the Congress did today was illegal," Susan Shalabi, PFA vice president, told Al Jazeera from Manama.
"It illegally blocked the motion which was proposed in accordance with FIFA's statutes. It is an illegal act by the highest body in FIFA.
"We've also seen clear intervention by the government in the business of the Congress. FIFA has suspended member states in the past due to government interference and now it has allowed Israel to do exactly the same."
FIFA's statutes forbid another member association playing on another territory without permission.
Israel argues that FIFA rules are unenforceable as there is no permanent border.
Palestinian leaders demanded that the Israeli federation be suspended from world football unless it orders the six teams - Beitar Ironi, Beitar Ironi Ariel, Beitar Givat Ze'ev, Beitar Ma'aleh Adomim, Hapoel Oranit and Hapoel Bik'at Hayarden - be relocated.