The State Department has given the office of the Palestine Liberation Organization an extension to allow an orderly shutdown of its operations, department spokesman Charles E. Redman said yesterday.

The Palestine Information Office here has until Dec. 1 to comply with an order to close issued Sept. 16 by the department, Redman said. The original deadline was yesterday.

Lawyers for the Palestinian office, which is funded by the PLO, asked for more time to overcome "practical and legal difficulties, primarily concerning their office lease and certain employment and contract obligations," Redman told reporters.

The office employs eight staff members, all of them either American citizens or legal residents, and its function is to distribute information about the plight of Palestinian refugees in Israeli-occupied territories and other Middle Eastern countries.

In ordering the closure, the State Department cited its concerns over terrorism committed by some groups associated with the PLO. The decision came after months of pressure from congressional leaders.

It sparked protests from Arab Americans, who accused the department of giving in to pressure from Jewish groups, and from civil libertarians who charged the U.S. government with violating constitutional freedom-of-speech rights.

The American Civil Liberties Union said in view of the extension it was postponing a lawsuit that was to have been filed yesterday against the State Department, demanding it rescind the closure.

An ACLU official said the extension would give the organization more time to compile documents to back up its contention that the closing was a violation of the First Amendment.