In an effort to improve longstrained U.S. Guyana relations, U.S. Ambassador to the United Nations Andrew Young said today that Washington will substantially increase financial assistance to this small Marxist country.

Officials accompanying Young on his two-day visit here said Washington plans to increase aid to Prime Minister Forbes Burnham's government from the current $1.1 million to $12.3 million over the next years.

The move is part of the Carter administration's new policy of giving a high priority to improving ties with the countries of the Carribean area.

Washington had displayed hostility toward this Idaho-size country of 800,000 after Burnham announced his intention in the early 1970s to make Guyana "the first orthodox Socialist state" in South America.

Since then, his government has been attempting to organize all sectors of Guyanese industry, agriculture and national life into a system of cooperatives where, in his description. "The consumers won the means of production in association with the state."

He also has said that this system leaves no future in Guyana for capitalism. His government's nationalization of foreign holdings, including substantial property owned by American companies, played a big role in the coolness of the Nixon and Ford administrations toward Burnham.

Since beginning his 10-nation Caribean tour. Young has argued consistently that it is in the United States' interest to help countries like Guyana overcome their severe economic difficulties. Otherwise, Young has said, these difficulties will produce instability in a region flanking the United States.

U.S. officials said the proposed Guyana aid package, which will require approval from Congress, will consist primarily of loans and grants for road-building, agricultural development and research and rural health improvements.

During his visit to Costa Rica yesterday, Young said the U.S. obligation to help victims of human-rights violations is so strong that, in some cases it justifies the risk of interfering with another country's sovereignty.

Comparing people who have been deprived of their rights with victims of an earthquake, Young said: "In many respects, human-rights assistance is like earthquake assistance. When the overwhelming human need cries out, national sovereignty becomes less important than the human need."

Young has made the Carter administration's controversial championing of human rights the dominant note of almost all his public utterances during the Caribbean tour.

His especially strong statement today came in response to a local reporter's question about what the United Nations can do about Uganda's President Idi Amin, whom Young previously had called a "murderer."

Conceding that an inability to deal with people like Amin is one of the U.N.'s weaknesses. Young endorsed a proposal made by Costa Rica for a U.N. human-rights commissioner to investigate and recommend action against governments that abuse their citizens' rights.

"The U.S. position is that as long as we are pursuing human rights openly and publicly, that when you do things across national lines, it's no defiance of sovereignty." The remark could have potentially sensitive implications here in Latin America, where resentment over past U.S. interference in the internal affairs of Caribbean and Central American countries is still strong.