After months of internal debate, the Reagan administration for the first time has said it is considering closing down the Palestine Liberation Organization's office in Washington.

State Department officials said yesterday that recent PLO actions, such as keeping Muhammad Abul Abbas, mastermind of the Achille Lauro hijacking in 1985, on its executive board, contributed to the decision on the politically sensitive issue.

The PLO's Washington office and its office at the United Nations are the target of legislation by members of Congress who argue that they are symbols of terrorism and therefore should be closed. Other members counter that shutting the office would violate U.S. precepts of freedom of speech and harm U.S. efforts to arrange peace talks between Israel and a Jordan-Palestinian delegation.

Secretary of State George P. Shultz wrote sponsors of the legislation last week that the administration opposes the bill because it would violate the president's powers in foreign policy.

But he added that the administration is considering closing the PLO's Washington office, the Palestine Information Office, on its own.

"Closure of the PIO as a 'foreign entity,' allowed up to now to operate by the U.S. government, would of course represent a symbolic shift in the U.S. government's relationship to the office, underscoring our disapproval of the PLO's retention of Abu Abbas on the Executive Committee, and undermine the PIO/PLO position and image in the U.S. and elsewhere," Shultz wrote in a July 31 letter to Sen. Charles E. Grassley (R-Iowa) and Rep. Jack Kemp (R-N.Y.), sponsors of the bills.

"Such a gain may be sufficient to warrant Executive Branch action in this regard at the appropriate time," Shultz added. His pronouncement followed months of internal discussions by State and Justice Department lawyers on the legal authority for such a move.

One knowledgable State Department official said U.S. authorities were "shocked" at the PLO's decision at a recent conference in Algiers to put Abu Abbas back on its executive board. The United States has sought his extradition on hijacking and murder charges since the hijacking of the Achille Lauro cruise ship in October 1985, during which an American was killed.

The Shultz letter noted that closing the PLO's U.N. observer mission would violate a U.S. treaty obligation and would lead to a probable defeat at the World Court and "a propaganda gain" for the PLO.

Shultz added that the Justice Department advised State that closing the PLO's Washington office wouldn't be barred by the First Amendment. But Shultz said Justice warned that members of the office could start a private U.S. entity and perform many of the same functions.

One State Department participant in the process said the Shultz letter was an effort "to make the bill go away."