The Carter administration has reached an agreement with Bulgaria on removing travel restrictions on their respective diplomats. This leaves the Soviet Union as the only Warsaw Pack country that continues to maintain a travel control system created during the Cold War period.

The American action was designed in part to demonstrate U.S. compliance with the 1975 Helsinki agreement on security and cooperation in Europe.

U.S. officials here conceded that its timing was linked to the current Belgrade conference where 35 nations are reviewing implementation of the terms of the Helsinki of its provisions calls on all signatories to "ease regulations to facilitate the movement" of diplomats, journalist and tourists on their territories.

The U.S.-Bulgarian accord, which went into effect with an exchange of notes Wednesday, was also a step toward improvement of Washington's relations with the Balkan country.

At the same time, Bulgaria has indicated willingness for the first time to begin negotiations on the settlement of about $15 million in pre-World War II Bulgarian bonds held by U.S. citizens. U.S. officials said the talks are expected to begin in December or in January.

The Bulgarian bonds were floated in U.S. capital markets in 1929, but the post-war Communist government of Bulgaria had so far refused to recognize any obligations of the old government.

The Carter administration, in a related move to improve relations with Eastern Europe, decided last week to return to Hungary the crown of St. Stephen, the 1,000-year-old symbol of Hungarian nation that has been in American hands since the end of World War II.

The lifting of travel restrictions means that American diplomats in Bulgaria can freely the exception of some border areas that Bulgaria regards as "security sensitive." In turn, Bulgarian diplomats will be able to move around the United States, with the exception of "installations of national security significance."

Travel restrictions were first imposed by the Communist governments of Eastern Europe in 1949. The U.S. government took reciprocal action. In 1963, Washington imposed a blanket curb on movements of Communist diplomats, declaring 350 countries or 18 per cent of continental U.S. territory as being off limits.

The off limits areas were dispersed in a way to effectively restrict movement by diplomats. The Bulgarians, for instance, could not go to Atlantic beaches near Washington since the main road to Rehoboth and Ocean City ran through an off limits area.

Since the early 1970s, the United States has actively sought to reach agreements on the lifting of restrictions on a reciprocal basis.

"Let's face it, the state of the art (of espionage) had gone beyong making these things effective," one American official said. "The restrictions are now merely an irritant."

Bulgaria was the last of Eastern European nations to reach such an agreement with Washington. The Soviet Union, however, has thus far rebuffed all U.S. proposals to begin negotiations on the lifting of travel restrictions.

The Soviets maintain a travel control system that applies to all foreigners. In 1974, Moscow made a gesture by lifting many restrictions on the movement of the U.S. ambassador to the Soviet Union; Washington in turn lifted restrictions on the movements of the Soviet ambassador here.