The Reagan administration exerted pressure on the Palestine Liberation Organization yesterday to come to terms quickly on laying down its arms in West Beirut.

A public statement by State Department spokesman Dean Fischer warned that "the risk remains high, if the various parties can't come to terms, that the fighting may resume."

The message, in the polite language of public diplomacy, was that an Israeli invasion of the Lebanese capital looms if a negotiated deal cannot be reached quickly.

Beneath the tip of this rhetorical iceberg, according to official sources, was a flurry of private messages and meetings here and around the world intended to advance a compromise between the PLO and the Lebanese government, and to induce Israel to agree to it.

President Reagan, speaking at a news conference last night, sought to "walk a very narrow line" on issues concerning the negotiations, which officials say are at a particularly delicate stage.

While refraining from criticism of Israel for invading Lebanon, Reagan said the move had surprised the United States, and he denied giving "a green light" for an Israeli invasion of Beirut.

Israel has put the administration on notice that it will end the cease-fire in and around Beirut unless the armed PLO presence ends quickly through diplomacy. In recent days, Washington has asked Israel publicly and privately for time, and a senior State Department official said yesterday that no specific deadline had been received from the Israelis.

A presidential spokesman denied a report that the White House had threatened sanctions against Israel, including an arms cutoff, if Israeli troops attack Beirut. Reagan himself declined to say what he could do in case of such an attack, citing the delicacy of negotiations.

The emphasis of U.S. diplomatic efforts turned to pressing for quick PLO decisions yesterday, following the Israeli cabinet decision to postpone further consideration of a Beirut attack.

Saudi Arabia has been among the major channels to the PLO and probably the most important pressure point on that organization, which has enjoyed Saudi financing and political support.

Yesterday, for the second consecutive day, Secretary of State Alexander M. Haig Jr. met Saudi Prince Bandar bin Sultan, whom the White House and State Department are using as a special channel to Saudi Arabia's King Fahd.

The Saudis are considered particularly important to the negotiations about the PLO's future because of an emergency meeting of six Arab League foreign ministers, including that of the PLO, which convened yesterday in the Saudi summer capital of Taif.

A decision at Taif to end the Palestinian armed presence in Lebanon would give important Arab legitimacy to an arrangement of the sort the PLO and the Lebanese government are discussing in Beirut, with the backing of the United States.

In a highly unusual situation, the State Department said Haig was still in overall charge of the Mideast diplomatic effort despite the announcement last Friday of his resignation. According to Fischer, Haig will continue to be in charge during a long holiday weekend starting today at The Greenbrier in White Sulphur Springs, W.Va.

Fischer said it was uncertain whether Haig would return to the State Department as secretary after the weekend and that this depended in part on the Lebanese situation.

Haig's designated successor, George P. Shultz, continued his tour of Capitol Hill yesterday for a meeting with Sen. Jesse Helms (R-N.C.), who later said he expects unspecified "changes" in U.S. policy under Shultz.

In another aspect of Mideast diplomacy, a message from Reagan to Egyptian President Hosni Mubarak was delivered in Cairo yesterday. According to Egypt's official Middle East News Agency, the message said the United States was engaged in intensive efforts to consolidate the sovereignty of the Lebanese government throughout Lebanon and to "safeguard the legitimate rights of the Palestinian people."

A message from Haig to Israeli Prime Minister Menachem Begin, delivered in Jerusalem by U.S. Ambassador Samuel Lewis, was yet another strand of diplomacy. Officials said the message summarized U.S. stands in the Beirut negotiations and aligned the United States with a continued PLO political presence in Lebanon, if it were acceptable to the Lebanese government.

Reagan said last night that the administration was reviewing use of U.S. weapons by the Israelis in Lebanon to determine, as required by law, if they were used for a legitimate "defensive" purpose as specified in the sales agreement.

A special study, which Reagan also mentioned, is investigating Israeli use of U.S. antipersonnel "cluster bombs," which are subject to tighter and more specific restrictions.