The administration, seeking to promote hope for renewed Mideast peace talks, is considering sending Assistant Secretary of State Richard W. Murphy to meet with a Jordanian-Palestinian delegation that would include at least one person widely regarded as a member of the Palestine Liberation Organization.

The proposal drew vehement protests from Israel yesterday. It also prompted U.S. officials to deny that they would abandon a longstanding commitment not to deal with the PLO until it accepts U.N. Security Council resolutions that acknowledge Israel's right to exist.

But the denials contained a disclaimer about the difficulty of defining what constitutes PLO membership. Specifically, the officials said it might be possible to argue that Nabil Shaath, one of four Palestinians proposed for the delegation, is not a PLO member, although he has been a close personal adviser to PLO Chairman Yasser Arafat.

While stressing that no decision on dispatching Murphy has been made, administration sources said many key policy-makers believe that such a meeting is the only way to break the deadlock impeding direct peace talks between Israel and Jordan.

Jordan's King Hussein proposed the meeting after White House talks with President Reagan last May. Despite Israeli objections, the United States said it was willing to honor Hussein's request if the joint delegation did not include PLO members and if the meeting gave hope of leading to direct Israeli-Jordanian negotiations on the future of Israeli-occupied Arab territories.

Murphy, assistant secretary for Mideast affairs, visited the region last month but refrained from meeting with a joint delegation after he was not given assurances that the hoped-for direct talks with Israel would result.

According to the sources, Murphy then told Secretary of State George P. Shultz that there is no chance of movement unless the United States meets with a delegation tentatively scheduled to include Shaath; Hanna Seniora, editor of an East Jerusalem newspaper; Fayez Abu Rahme, a Palestinian lawyer from the Gaza Strip, and Henry Catton, a Palestinian historian living in Europe.

Murphy is understood to have told Shultz that, if the meeting is held, he believes that the PLO then would recognize the U.N. resolutions dealing with Israel's right to exist.

His recommendation that the United States test the PLO's intentions reportedly has been backed strongly by several key State Department officials, including Michael H. Armacost, undersecretary for political affairs.

However, Shultz is understood to be uncertain about whether to accept Murphy's recommendation, and the plan has been referred to the White House for further consideration.

Underscoring the proposal's controversial nature is the proposed inclusion of Shaath, a Cairo resident who has been a close Arafat adviser on political strategy and has represented the PLO at international meetings.

Despite his background, administration officials said yesterday that, because the PLO is an umbrella organization of several Palestinian groups and "doesn't issue membership cards," it is possible to make different interpretations about what constitutes membership.

Referring to Shaath, one official said, "He's not on the PLO executive committee, he's not head of any of its factions, he doesn't have an official title. He might well fall within the parameters we've set for defining a non-member."

However, the same official, while stressing that he does not know what decision will be made about a meeting, said, "Whatever is done will be something that Israel can live with. The object is to get direct negotiations, which [Israeli Prime Minister] Shimon Peres wants. We're not seeking a back-door recognition of the PLO."

Diplomatic sources said Armacost reiterated those assurances yesterday to Israeli Ambassador Meir Rosenne.

But, the sources added, Rosenne repeated Israel's opposition to any U.S.-Palestinian meeting at which it is not represented. Referring to the four Palestinians slated for the proposed meeting, the ambassador reportedly said Peres considers only Seniora and Abu Rahme to be genuine non-PLO members.