A long standing territorial dispute between Libya and Tunisia flared up with new bitterness this weekend when an American-owned oil-drilling rig began operating on behalf of Libya in waters claimed by Tunisia.

Each country accused the other of sending naval units to the area in the Gulf of Gabes to enforce its claim. Earlier this year, when the Libyans engaged in Italian rig to drill in the same place, the Tunisians sent a warship to force the Italians out. Their departure brought a furious protest from the Libyan government of Col. Muammar Qaddafi, which has threatened economic reprisals against Italy for abandoning the drilling site.

This time Tunisia has complained to several countries, including the United States, and to the Arab League about the Libyan move.

While not explicity threatening millitary action, the Tunisians have talked in diplomatic notes about refusing to accept a "fait accompli" and "reserving the right to take appropriate action."

The drilling rig is owned by the American firm of Reading an Bates, but it is not clear from reports reaching here whether there are any U.S. citizens working on it. On contract to Libya's national oil company, it was towed into position last week to drill on a part of the Continental Shelf that has been in dispute between the two countries since the 1960s.

Tunisian diplomats here say that their country complained to the American embassy in Tunis and that the State Department warned the rigs operators that they were working in disputed waters. But the operators went out anyway, the Tunisian diplomats say, under the protection of two Libyan warships.

The dispute is an urgent matter for Tunisia, so much so that its ailing president, Habib Bourguiba, personally received the Libyan ambassador yesterday to discuss it. The Tunisian Parliament met in closed session this morning to consider the crisis, and the Cabinet was to take it up later in the day.

Last year the two North African neighbors agreed in principle to submit the boundary dispute to the International Court of Justice in The Hague but did not actually do so. The Tunisians insist that they are ready to accept the judgment of any impartial arbiter and accuse of Libya of trying to obtain by unilateral action what it is not entitled to in law.

While there are many points of disagreement between the two countries, the Tunisians appear to be especially bitter about this one, saying that they need the oil and the Libyans don't.

As a Tunisian communique put it yesterday, "No one in our sister country. Libya, nor in Tunisia, nor in the Arab of Islamic world, or in the whole world could believe that the Libyan government needs to be in a hurry to exploit unilaterally a disputed zone."

Tunisian sources say they believe that Libya, which has vast oil wealth for a nation of only 2 million, is producing at far less than capacity from its existing fields and could well afford to await the outcome of arbitration before proceeding offshore.