The Honduran government said today that it would not allow the U.S. Embassy here to administer the $27 million of nonmilitary aid approved by Congress for Nicaraguan rebels fighting to overthrow the government in Managua.

The statement by Foreign Minister Edgardo Paz Barnica raised questions about how the aid would be delivered to the rebels, who are known as contras, or counterrevolutionaries.

The contras currently bring arms and other supplies through Honduras to base camps along the border with Nicaragua. The existence of this supply route is an open secret, but the government here publicly denies that the contras operate on Honduran territory because it does not want to admit that it is helping the effort to overthrow the Sandinista government.

The Honduran position appeared to make it necessary for the U.S. government to hand over the aid to the rebels somewhere outside Honduras, according to sources familiar with the issue.

The Reagan administration is considering what mechanism will be set up to deliver the aid, and a decision is expected within a week or two. A U.S. Embassy spokesman declined to comment on Paz Barnica's statement, saying he could not say anything about the aid until Washingon decides how the program will be set up.

But nonofficial sources close to the embassy here said the embassy does not want to have a role in handling the aid because such involvement would embarrass the Honduran government. The United States has to do its part to help the Hondurans "save face" on the issue, these sources said.

Paz Barnica said he was "completely" unaware of any plans for the embassy here to handle the aid. But he said that the assistance was a concern only of the United States and the contras and that Honduras should be left out of it.

"I do not believe, then, that the government of Honduras is going to accept that the U.S. Embassy in Tegucigalpa would deliver money to people who are fighting against the regime of a neighboring country," Paz Barnica said at a news conference.

A U.S. role in Honduras in providing the aid, he added, would be "incompatible with the principles of nonintervention and self-determination of peoples."

Congress approved the nonmilitary aid for the contras in June after several months of debate and controversay. The vote marked a resumption in the flow of official U.S. aid to the contras, which had been cut off last year.

Under the previous aid program, about $80 million of arms and other assistance was supplied to the contras by the CIA. The aid was channeled through Honduras, but the program was covert, and the government here was able to deny that it existed.

The U.S. aid approved in June is not covert, and Congress specifically barred the CIA and the Defense Department from administering it. The dilemma facing policy-makers is how to manage a public aid program when the aid has to be delivered to forces in the field by clandestine means.

"Both the embassy and the Honduran government are caught between a rock and a hard place," a source familiar with the issue said.

One possibility under consideration was to deliver the aid to the contras in Miami, which is the home of several rebel officials, including Adolfo Calero. He is president of the Nicaraguan Democratic Force, the largest contra group, and has played a leading role in raising funds from private sources during the past year.

Calero also is one of three top leaders of the United Democratic Opposition, an umbrella organization that also includes Nicaraguan civilian opposition leaders Arturo Cruz and Alfonso Robelo. The umbrella group is considered a likely channel for the new U.S. aid.