The Israeli accusations came after a United Nations committee that oversees non-governmental organizations voted to approve UN accreditation for the PRC, which Israel's mission said was not only linked to Hamas but promoted "anti-Israel propaganda in Europe."
"We announce that PRC is considering legal action against the Israeli delegation at the UN," the group said in a statement circulated to the 19-member UN Committee on Non-Governmental Organizations.
"We also hold them accountable for the safety and security of our members worldwide," the group said. "Such allegations and defamation where we are described as terrorist and affiliated to Hamas are dangerous, baseless and will have negative ramifications on our work and members."
The statement offered no details on the type of legal action the group might take against the Israeli mission.
The Israeli mission did not have an immediate response to the PRC's threat. On Monday the mission said Israel had banned the PRC in 2010 because of its ties to Hamas, labeling it "an organizational and coordinating wing of Hamas in Europe" with members that include senior Hamas officials.
The PRC operates as a legal entity in Britain. The British mission did not react to Monday's vote in the UN NGO committee.
The United States and European Union have designated Hamas, the de facto authority of the Gaza Strip, a terrorist organization. The internationally recognized Palestinian Authority controls the West Bank.
The PRC statement said the Israeli allegations had no credence and were solely based on Israeli intelligence and other sources from within Israel. It added that there was no corroborating evidence from a third country.
The PRC said it would soon send an official letter of protest to UN Secretary-General Ban Ki-moon and the 54 member states of the UN Economic and Social Council (ECOSOC), which has final say on NGO-related matters.
On its website, the PRC describes itself as "an independent consultancy focusing on the historical, political and legal aspects of the Palestinian Refugees."
Official UN status as an NGO gives groups access to UN premises and opportunities to attend or observe many events and conferences at United Nations sites around the world.