AFC president Sheikh Salman bin Ebrahim Al Khalifa said that a deadline for ending the matter had been repeatedly put off and that Palestinians merely wanted to see "football played on their land".
The dispute centres on six teams from lower divisions of the Israeli league who are based in settlements on the occupied West Bank and play their matches there.
The Palestine Football Association (PFA) says this is contrary to FIFA statutes which state that a member country's teams cannot play matches on the territory of another association without permission.
Israeli settlements are considered illegal under international law, although Israel disputes this.
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The PFA has also complained that Israel hampers its activities, including limiting the movement of players between the West Bank and Gaza, and that it has barred some international travel.
Israel has cited security concerns for its actions and the Israeli FA, which is a member of European soccer body UEFA, says it is not responsible for the actions of its government.
The AFC said in a statement that its executive committee had "backed a recommendation to insist FIFA seek an urgent resolution to the ongoing Palestine issues with Israel".
It called on FIFA to apply "the relevant FIFA statutes as soon as possible".
“Palestine is a Member Association of the AFC and all they want is to see football played on their land," said Sheikh Salman.
"We would like to see a definite deadline set, as in the past the deadline has been extended again and again. We all feel strongly that this issue should be resolved.’
The PFA called on the FIFA Congress two years ago to suspend Israel but was persuaded to drop the motion at the last minute.
(Writing by Brian Homewood)
