Egyptian President Hosni Mubarak believes that Jordan's King Hussein and Palestine Liberation Organization leader Yasser Arafat want to respond favorably to President Reagan's Mideast peace initiative and are working to win the backing of the various PLO factions, a senior Egyptian official said yesterday.

The official spoke with reporters about Mubarak's talks here with Reagan on condition that he not be identified. At Thursday's White House meeting, Mubarak stressed that unless Israel withdraws its troops from Lebanon, sentiment in the Arab world will be solidly against Hussein entering negotiations with the Jewish state, and the Reagan initiative would almost certainly become a dead issue.

But, the official said, if an agreement is worked out on withdrawing Israeli and other foreign forces from Lebanon, both Hussein and Arafat would be disposed to see the proposal set forth by Reagan on Sept. 1 as the best chance for resolving the Arab-Israeli conflict in a manner that satisfies Arab aspirations for a Palestinian homeland.

In Mubarak's view, he said, the main obstacle to Hussein representing the Palestinians in expanded talks about the future of Israeli-occupied Arab territories is not Arafat but the differing PLO factions.

"Arafat is a very moderate man," the official said. "He is convinced of the Reagan initiative. Also King Hussein is convinced. They may speak of the Fez initiative, but they support the Reagan initiative." The Fez initiative is an Arab League declaration calling for an independent Palestinian state under PLO leadership.

Mubarak has endorsed the Reagan initiative, which rejects the idea of an independent Palestinian state and calls instead for the West Bank and Gaza Strip to gain independence "in association with Jordan."

Hussein is engaged in delicate negotiations aimed at getting a green light from the PLO and Arab states such as Saudi Arabia to join Egypt and Israel in a broadened peace process. However, the movement has been slow, and Mubarak stressed to Reagan Egyptian fears that time is running out on the chances for successfully launching the U.S. plan.

The problem, the Egyptian official said, "is with the differing PLO factions that take different positions and are contradicting each other publicly." This was a reference to the fact that the PLO is an umbrella organization including some groups unwilling to abandon the idea of an independent Palestinian state or to forswear armed struggle against Israel.

The official noted that the top PLO leadership is to meet in Algiers on Feb. 14 and said he hoped that at that time the Palestine National Council, the PLO's parliamentary body, "will reach a conclusion" permitting Hussein and Arafat to strike a deal on Jordanian participation in the peace process.

"Otherwise, they will lose a lot," the official warned.

In response to questions about whether Israel might be dragging its feet deliberately on withdrawing from Lebanon because Israeli Prime Minister Menachem Begin opposes the U.S. proposals, the official said Mubarak had urged Reagan to do everything possible to convince the Israelis that they should pull out of Lebanon as quickly as possible.

In public remarks earlier yesterday after a visit to Congress, Mubarak said: "I am urging Israel to withdraw from Lebanon and to go to the core of the problem, which is the Palestinian problem. I'm praying to God that Israel should withdraw from Lebanon so as to have peace in the whole area, because peace is precious not only for Israel but for all the Arab countries . . . . "

The official also defended Mubarak's action in recalling the Egyptian ambassador from Tel Aviv after the Israeli invasion of Lebanon led to the massacre of Palestinian civilians by Lebanese Christian militiamen. He said it was the "minimum" that Mubarak, as head of an Arab country, could do in the face of demands that he take stronger steps such as breaking relations with Israel.

At a meeting yesterday with American Jewish leaders, Mubarak reiterated that he is committed to maintaining peaceful relations with Israel and intimated that the Egyptian ambassador will return to Tel Aviv once the question of Israeli withdrawal is settled.