President Carter gave the green light yesterday to a controversial $75 million aid package for Nicaragua by finding that the Marxist-oriented Sandinista government is not aiding acts of violence or terrorism in any other countries.

Administration officials consider the aid package vital to their entire Central American policy, which attempts, by maintaining friendly relations, to keep Nicaragua and other vulnerable nations from falling into the Cuban camp.

Right-wing opponents of the package argue that Nicaragua is already lost to Cuba and that any American aid only bolsters a regime that is a threat to other non-Marxist nations of the region.

The decision, which may become an issue in the presidential campaign, was instantly attacked by Rep. Robert E. Bauman (R-Md.).

"I believe that [Nicaragua] is not only directly engaged in terrorism in Guatamala and El Salvador, but also being used as a conduit for Cuban arms," he said.

"The administration does not intend to abandon the vital Central America region to Cuba and its radical Marxist allies," the White House said yesterday.

Administration officials argued that the $75 million does not guarantee that Nicaragua will not turn its back on the United States and abandon those freedoms it still maintains, but that "failure to go ahead with the aid would have made Nicaragua go in the opposite direction."

Delay has already been costly, these officials said. The administration was ready shortly after the Sandinistas won their civil war in July 1979 to offer aid, but strong opposition checked it and Congress eventually added the requirement that Carter certify that Nicaragua's government was not harboring terrorists or exporting revolution before it could be given aid.

"It is clear that the delay has had a radicalizing impact," one administration official said. "These people down there are hanging by their fingertips."

About 60 percent of the package will go to private-sector businesses -- primarily agricultural, the White House said.

The civil war left Nicaragua in desperate need of aid, and the long delay in approving this aid package was used by some elements in the country who seek to undermine the free-enterprise element of the economy and the existing political pluralism, administration officials said.

In order to certify that Nicaragua is not supporting violence elsewhere in the hemisphere, the intelligence community and U.S. embassies in the region were asked to submit evidence. "The diverse information and opinions from all sources were carefully weighed," the White House said.

Administration officials who briefed a small group of reporters said that the Defense Department, State Department and National Security Council all agreed that there was no conclusive proof that Nicaragua was aiding terrorists.

Administration lawyers advised that the certification could be granted in the absence of conclusive proof, they said.

The Nicaraguan leaders make no secret of their close ties to Cuba, but there are many Nicaraguans committed to democratic freedoms. Political pluralism, free enterprise and freedom of the press have survived the first post-revolutionary year in Managua, the White House said.

The administration made its aid to Nicaragua the first major step in an effort to increase aid throughout Central America. Aid to El Salvador, in which extremists of left and right are battling -- often at the expense of the middle -- was raised to $72 million. The entire new package for the region totals $250 million.

About $21 million of the aid to Nicaragua has already gone out since it was not given to the government and therefore not contingent on Carter's certification.

Administration officials said loan agreements for the remaining $54 million, which will be administered by the Nicaraguan Central Bank, will be signed next week.

Although the money is scheduled to go out quickly, Congress has stipulated that the president must hold up any outstanding part of the aid if he discovers in the future that Nicaragua is promoting terrorism.

Carter's decision is likely to be opposed by his Republican challenger. Ronald Reagan is running on a platform that says:

"We deplore the Marxist Sandinista takeover of Nicaragua and the Marxist attempts to destabilize El Salvador, Guatemala and Honduras. We do not support U.S. assistance to any Marxist government in this hemisphere, and we oppose the Carter administration aid program for the government of Nicaragua."