King Hussein welcomed Palestine Liberation Organization Chairman Yasser Arafat here today and began several days of talks on joint relations that in large measure will determine how the two key leaders approach President Reagan's Middle East peace initiative.

Hussein was seeking an understanding that Arafat would not condemn him if the king went ahead and held talks with Washington on its plan for a self-governing Palestinian entity associated with Jordan, an informed Jordanian source said. Hussein risks being branded an Arab traitor if he embraces the Reagan plan without clearing it properly.

Arafat suggested on his arrival that he was looking for something more than what Reagan and Hussein are offering. He said in a brief airport statement that he had come "to discuss implementing the resolutions of the September Fez summit," which provide for establishment of an independent Palestinian state.

U.S. officials have said they would watch closely the negotiations here for signs of whether Jordan was prepared to join fully in the U.S.-mediated peace process, in part because the administration cannot apply any pressure on Israel to cooperate until Jordan says it will participate.

Hussein is expected to visit Washington before the end of the year on what has become a regular annual visit, and the trip could provide the opportunity for celebrating a new phase in U.S. Middle East diplomacy if all goes well, sources indicated.

No details were available here tonight on the substance of the talks, but Radio Jordan reported that the leaders discussed "ways and means aimed at saving the territories and kinsmen in the occupied lands by securing an Israeli withdrawal through a just and lasting settlement."

Arafat, who has been on a tour of Arab capitals since the PLO completed its evacuation from Beirut five weeks ago, flew into Amman from Bahrain at about noon. Hussein received him at Basman Palace, seat of the royal court, and they met for about five hours both privately and with aides.

Arafat's decision to stay several days -- at least until Monday, according to Jordanian sources -- reflected the importance given to the talks here. The two leaders are seeking to chart Palestinian-Jordanian relations following the PLO's eviction from Lebanon, and both have much at stake.

For Hussein, the issue is ending the principal threat to his nation's stability by resolving the Palestinian issue and effectively making peace with Israel. If he moves too fast, he risks being ostracized as was Egypt.

Arafat, on the other hand, is looking for a focus for his organization's efforts to find a homeland in Palestine now that his guerrillas have been scattered to eight Arab countries. If he yields too much, he risks losing the backing of the PLO's most radical branches.

Hussein, who welcomed the Reagan initiative as a positive step, has been laying the groundwork for the talks with Arafat in the past three weeks. On Sept. 20, he delivered a speech proposing a Palestinian entity in "federation" with Jordan and a plebiscite to approve it. On Thursday, he pardoned 736 Palestinian fighters who battled with his troops in "Black September" of 1970, when Jordan booted out the PLO because its radicalism threatened the king's moderate rule.

Memories still linger from those difficult days, and U.S. officials believe that the Reagan plan was particularly attractive to the king in part because it rules out a Palestinian state. The Jordanian source stressed that Jordan would wish to preserve responsibility for coordinating military affairs with any Palestinian entity, while the Palestinians would have self-government in other respects, a separate flag and passport.

A key issue is who will speak for the Palestinians in any coming negotiations. Hussein has said that he will not seek to represent the Palestinians without Arab League authorization, which Jordan sought but failed to obtain at the Fez summit. The league stuck to the Rabat declaration of 1974, which named the PLO as the sole representative of the Palestinian people.

Hussein has indicated, however, that he might seek some form of bilateral Jordanian-Palestinian initiative as a first step toward taking on the mantle as Palestinian spokesman. Radio Jordan said the talks considered "the joint Jordanian-Palestinian effort in particular because of the special and distinguished relations that link them."