TUNIS, Tunisia (AP) _ U.S. Ambassador Robert H. Pelletreau Jr. made a brief telephone call to PLO headquarters this morning, launching the dialogue authorized by Secretary of State George P. Shultz, spokesmen for the two sides said.

Adnan Siddiqi, information officer at the U.S. Embassy, said the telephone call was made to start what Shultz said Wednesday will be a ''substantive dialogue'' with the Palestine Liberation Organization.

In Washington, a U.S. official said Pelletreau had called the director general of the political section at the PLO's Tunis headquarters to try to make arrangements for talks.

The official, who spoke on condition of anonymity, said no date for the talks was set but ''we're sure the PLO will try hard to have them take place as soon as possible.''

Another U.S. official said the session could be held as early as tomorrow and certainly within the next few days.

Siddiqi, reached by telephone from Paris, said he did not know who Pelletreau spoke to, what they discussed, or when the first face-to-face talks might be arranged.

Abu Yahia, director of the PLO political section, confirmed in a telephone interview from Paris that the conversation took place but declined to identify the PLO official who spoke with Pelletreau.