East Germany, in a major effort to improve relations with the United States, has agreed to settle all pending humanitarian cases between the two countries and has proposed a wide range of expanded trade, government and cultural contacts.

The moves, detailed yesterday by U.S. and East German sources, come shortly before next month's 35-nation conference in Belgrade to review compliance with the 1975 Helsinki agreement. They clearly appear intended to put the East German governmentin good standing with the Carter administration.

U.S. officials described the proposal for expanded contacts as "significant" and said that in agreeing to settle the humanitarian issues, East Germany has "taken a giant step" toward solving problems posed by its restrictive emigration policies.

East Germany, although one of Eastern Europe's most rigid regimes and the Soviet Union's most loyal ally, is nonetheless intensely interested in increasing trade with the United States.

A good record on humanitarian issues and demonstration of a readiness to expand contacts would, in East Germany's view, improve its chances of winning congressional as well as presidential approval for preferential trade treatment.

Notification of East Germany's willingness to allow several dozen East German citizens to emigrate to join relatives in the United States was given to the State Department last month by East German Ambassador Rolf Sieber, according to diplomatic sources here.

On May 12, East German Foreign Minister Oskar Fisher gave Sol Polansky, the U.S. charge d'affairs in East Berlin, a list containing nearly a dozen specific proposals for improved relations in a number of fields.

U.S. officials said that the humanitarian cases settled by East Germany involved about 60 persons. Most of these want to join relatives here; a few are engaged to marry Americans.

The East German decision does not, however, include persons who apply in the future to emigrate, U.S. sources said, nor does it deal with a related problem: East Germany's reluctance to allow its citizens to come to the United States temporarily on cmpassionate visits to ailing or aged relatives.

Much of what East Germany proposed in the list presented by its foreign minister had been requested piecemeal previously, U.S. officials said, but the State Department considers its package presentation now as an "important development" and is "looking at it very carefully."

East German officials consider the proposal a "significant statement" of their government's intention to "develop the range of bilateral relationships with the United States."

East Germany has proposed:

Doubling the the educational exhange program recently increased from 20 man-months of study to 40; broadly expanding the language exchange program and moving toward a full cultural pact.

Regular consultation between U.S. and East German officials at all levels; visits to East Germany by a high-ranking State Department official and a congressional delegation and an invitation to a top East German to visit the United States.

Treaties governing mail and shipping between the two countries and declaration of intent by both governments to promote trade with each other actively.

Improved visa, travel and working conditions for journalists.

Conclusion of a consular agreement.

The consular agreement is expected to be the most difficult issue to resolve. Few Western countries have been willing to recognize formally East Germany's right to act in consular matters for residents of East Berlin, which is still considered under separate administration since World War 11.

East Germany, whose debt to the West has grown to about $5 billion, made a strong bid at the recent Lipzig trade fair to arrage barter deals with American companies, to use goods rather than money to buy American products.

Joint committees for trade were recently established and a 13-member East German trade delegation is to begin a visit to the United States June 13.