The letter made no mention of possible ICC action, which in any case would first require a series of steps by the Palestinians and the court.
A Palestinian case at the ICC could also expose Abbas' main Palestinian rival, the Islamic militant Hamas, to possible war crimes charges for its indiscriminate rocket fire from Gaza on Israel.
Hanan Ashrawi, a senior PLO official, said the Palestinians were encouraged by the recent diplomatic sanctions against Israel, but that the international community must go further.
Among other steps, she said the European Union should reconsider its association agreement with Israel that grants the Jewish state considerable trade benefits. She said the EU should also take harsher measures against products from Israeli settlements.
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