King Hussein of Jordan's public call for the Palestine Liberation Organization to recognize Israel's right to exist has aroused little enthusiasm in government circles here. But the king's recent diplomatic forays are causing much ferment inside the opposition Labor Party and among Palestinian notables on the occupied West Bank and Gaza Strip.
The king told a BBC-TV interviewer on Nov. 4 that PLO recognition of Israel ''would be of great help to our joint cause.'' When King Hussein met PLO leader Yasser Arafat in Amman in October they discussed but did not finalize a Jordanian-Palestinian federation plan. But the king has said he will not negotiate without a PLO green light. If the PLO recognized Israel, this would meet United States conditions for a US-PLO dialogue and put more pressure on Israel.
The Israeli government is cool to Hussein's remarks because he wants to negotiate on the basis of the Reagan peace initiative, not Camp David. The Reagan proposals, while not contrary to Camp David, spell out US positions previously left vague. For example, they call for freezing Jewish settlement on the West Bank and specify US support for returning West Bank land to Jordan.
Israel opposes both ideas. On Sunday, Prime Minister Menachem Begin ordered Israeli Ambassador to the US Moshe Arens to protest sharp US criticism of Israeli settlement policy. But the Labor Party supports territorial compromise with Jordan on the West Bank. Labor party leader Shimon Peres has called on the government to make ''a wise and speedy move'' to bring Jordan and Palestinian representatives to the bargaining table.
West Bank sources say Hussein has dropped his unwillingness to negotiate with Begin. The reason: a fear, shared by West Bankers, that Israel is rapidly completing de facto annexation of the occupied areas.