Israel, moving a step closer to acceding to the U.S. demand that it withdraw its forces from West Beirut, agreed today to open discussions with the Lebanese Army "as soon as possible" on a troop pullback from the city.

Senior Israeli officials said their aim was to work out a procedure for replacing the Israeli forces in the city with Lebanese troops. No timetable was given for the discussions, but the officials said that the transfer might begin in about a week.

While the agreement indicated Israeli willingness to withdraw from the city soon, it fell far short of meeting the Reagan administration's demand yesterday for an immediate pullback and left open the details of what Israeli officials said would be an "orderly" transfer of key positions in the city.

A statement announcing Israel's intention to begin the discussions with the Lebanese Army was issued following a long meeting that U.S. envoy Morris Draper held here with Israeli Foreign Minister Yitzhak Shamir and Defense Minister Ariel Sharon.

Draper left the meeting about two hours before the statement was issued, apparently to confer with officials in Washington. Israeli officials said there was a "degree of agreement" by the United States with the procedures that they had proposed, and Shamir told reporters as he left the meeting that "real progress had been made." He did not elaborate.

In Washington, State Department officials were understood privately to see some indications of Israeli willingness to begin talks on a withdrawal.

Israeli troops entered West Beirut early Wednesday following the assassination Tuesday of Lebanese president-elect Bashir Gemayel, and the Cabinet late last night turned aside the U.S. demand for a withdrawal. The government declared that Israeli forces would leave the Lebanese capital when, in Israel's judgment, the Lebanese Army can assume control of the positions in the city now held by Israeli troops.

Sharon was reported yesterday to have strongly opposed an immediate Israeli pullout. Leaving the meeting with Draper, he declined to answer questions but said, "Our troops are holding key positions in West Beirut . . . . We have done this as a result of the cruel murder of president-elect Bashir Gemayel. We believe that this will bring the elimination of the remaining terrorists still operating in West Beirut."

Sharon's comments after meeting with Draper were less severe than those attributed earlier in the day to Israeli Chief of Staff Lt. Gen. Rafael Eitan. Eitan was quoted in the newspaper Maariv as saying of West Beirut, "Now what has to be destroyed will be destroyed. And who has to be arrested will be arrested."

The Cabinet yesterday charged that about 2,000 Palestine Liberation Organization guerrillas had remained in West Beirut after the withdrawal of the bulk of the PLO forces under the evacuation agreement negotiated by U.S. special envoy Philip C. Habib. Sharon is widely assumed to have welcomed the opportunity to order his forces into the city in an effort to eradicate guerrillas who allegedly remain.

While Prime Minister Menachem Begin said yesterday that Israel had learned only this week of the large number of PLO guerrillas still in West Beirut, Israeli radio tonight quoted Deputy Chief of Staff Gen. Moshe Levy as saying that it had long been obvious that Israel would have to make sure that the remaining guerrillas were removed from the city.

Israeli officials said that the Cabinet last night had authorized Shamir and Sharon to propose the meetings between Israeli and Lebanese Army representatives. At those meetings, according to the statement issued by Foreign Ministry spokesman Avi Pazner, "detailed plans will be exchanged for the evacuation of Israeli positions when the Lebanese Army will be ready to assume control over them."

Israeli officials said they assumed the Lebanese Army was capable of maintaining order in Beirut and willing to take over from the Israeli forces.