This socialist republic on the northeast coast of South America is eager to improve ties with the United States.

After 10 years of deteriorating relations, it sees the possibility that the United States, under President Carter, will adopt a more friendly attitude toward Guyana and its socialist system.

Forbes BUrnham, Guyana's prime minister for the past 15 years, says he would like to meet Carter at an early date for "serious talks" on a variety if issues which would surely include U.S. help in a vast development project that could bring the former British colony "into the 20th century."

In the course of an interview on the veranda of Belfield, his ocean-front villa 30 miles east of here, Burnham asked that the United States:

Express tolerance for Guyana's socialist experiment which "is not an act of aggression or hostility toward the United States," but a program in the country's self-interest.

Recognize that "the American experience is not necessarily valid for other people in different climes and different circumstances."

Burnham would like the United States to recognize that "small countries have a right to national and human dignity, and to make their own decisions."

The prime minister also recognizes Gyana's dependence on outside assistance. Guyana needs to put together a package of international financing for the development its rich interior - with its minerals, forests, and hydroelectric potential.

"If we can put the package together," he added, "we will move into the 20th century."

Burnham admits, however, that the cost is staggering - $1 billion for the first stage of a huge hydroelectric plant, a bauxite smelter for the country's nationalized alumnium industry and a highway opening up timber reserves.

Burnham feels the United States has misunderstood the direction of his government. Yes, he says, it is socialist, but he is quick to note that there is a substantial private sector here "and there will continue to be."

Guyana recognized Cuba in 1972, along with Barbados, jamaica, and Trinidad and Tobago, - an action then condemned by the United States. The Prime Minister noted that the United States now is moving in the same direction. After all, he asks, "Don't we have the right to decide who we will recognize?"

Guyana also has good relations with the Soviet bloc. China and the newly independent countries of black Africa.

To pay for the project will be a big task, but Burnham says he is convinced that uyana is a good risk. The country is saddled with high energy costs that would be shaved considerably by introduction of hydroelectric power on a vast scale. Moreover, the bauxite smelter would generate substantial revenues.

Burnham was the winner in a struggle for power with Marxist Cheddi Jagan prior to independence from Britain in 1966, thanks in part to covert U.S. and British support. Subsequent elections retaining Burnham in power have been denounced by Japan's party as fraudulent.