The Reagan administration, struggling to keep alive hopes for a diplomatic solution to the Lebanon crisis, urged Israel yesterday not to attack Palestinian fighters in West Beirut. But it acknowledged that the United States cannot control events in the Lebanese capital.

Only hours later, Israeli armor was reportedly advancing into West Beirut. However, an Israeli Foreign Ministry spokesman denied there was any substantive movement of Israeli forces into the city.

"These tank movements are unhelpful," White House assistant press secretary Mark Weinberg said last night. "Further military movements of this type are inconsistent with the maintenance of a cease-fire in place."

Earlier in the day, State Department spokesman Alan Romberg, in a follow-up comment to the views expressed Monday by President Reagan to Israeli Foreign Minister Yitzhak Shamir, said:

"The United States does not want an attack against Beirut. At the same time, regardless of what we want, while we can influence events, we cannot ultimately control them. Therefore it is of the utmost importance that the cease-fire in place around Beirut be maintained so that negotiations can proceed and that those negotiations move forward on an urgent basis."

Romberg's statement, made while Shamir was still in Washington and before last night's Israeli advance, underscored anew the growing concern in the administration that Israel is running out of patience with the efforts of Reagan's special envoy, Philip C. Habib, to negotiate the removal of Palestine Liberation Organization forces from West Beirut and ultimately from Lebanon.

Following the Reagan-Shamir meeting Monday, the White House made clear that it wants Prime Minister Menachem Begin's government to give Habib more time and to refrain from actions, such as increasing Israeli military pressures on Beirut, that complicate his task.

However, while Reagan's message was known to have elicited an Israeli promise to hold back for the time being, Shamir was understood to have made clear that Israel would not forswear its military option and was not disposed to wait on Habib indefinitely.

Israeli sources privately insisted that neither Reagan nor other senior administration officials resorted to threats or tough talk in the meetings with Shamir, who is to leave Washington this morning. According to these sources, Shamir is leaving with the impression that the administration still shares Israel's goal of forcing the PLO out of Lebanon and that even an Israeli resort to force would not put permanent strains on the relationship between the two governments.

While no one seems certain of the effects that an all-out attack against Beirut would have on U.S.-Israeli relations, the Israelis were understood to be encouraged by Shamir's meetings yesterday with the Senate Foreign Relations Committee and the House Foreign Affairs Committee.

Sources present at the two closed sessions said a variety of views were expressed about Lebanon, including considerable concern about the need to avoid further fighting and casualties. But the sources also agreed that the meetings, while containing some coolness, were devoid of the heated and frequently angry exchanges that took place when Begin visited here in late June. Shamir, who talked with reporters at a luncheon of the Overseas Writers, fielded questions about U.S. concern by saying "there are some problems . . . about our tactics in Beirut." But, in response to a question about whether Reagan was seeking to "crack down" on Israel, he replied: "I don't know of any cracks."

He reiterated the Israeli positions that the PLO must leave Lebanon, that his government would prefer to see a withdrawal accomplished through peaceful diplomacy and that Israel is doing everything it can in Lebanon to avoid unnecessary civilian casualties and suffering.

Shamir contended that Arab estimates of casualties were "grossly exaggerated" and said that while he could not give any figures for Beirut, he was aware of "some assessments" in the foreign services of other countries that civilian deaths caused by the Israeli incursion into southern Lebanon were about 1,000.

That appeared to be a reference to secret estimates made recently by the United States on the basis of reports from the U.S. Embassy in Beirut and a visit to Lebanon by M. Peter McPherson, head of the Agency for International Development. These reports are understood to have concluded that in southern Lebanon, as distinct from Beirut, between 1,000 and 1,100 Lebanese civilians were killed.

However, these same reports also are known to estimate that from 2,000 to 3,000 Palestinians also were killed in southern Lebanon and that, because of Israeli refusal to allow access to areas of Palestinian concentration during the early fighting, there is no way of telling how many were Palestinian guerrillas and how many noncombatants.