The Food and Drug Administration has refused to ban 10 widely used food, drug and cosmetic dyes linked to cancer in laboratory animals, saying that although it cannot prove the dyes are safe, it also does not believe that they are dangerous.

The agency said its decision, allowing continued use of the dyes while more studies are conducted, will stand for at least a year, and, for some of the dyes, may run through the remainder of the Reagan administration.

In a letter written Friday and released yesterday, the FDA denied a petition from the Ralph Nader-organized Health Research Group, which sought an immediate ban on grounds that the dyes represent a public-health hazard.

FDA Commissioner Frank E. Young said that further study of nine of the dyes is needed, even though they have been under study since 1960. Those studies will take from one to five years more, he said.

"In each case, I have concluded that the public health will not be endangered by the continued marketing of these color additives while these scientific, legal and policy issues are addressed," Young said.

The exception is a food, drug and cosmetic dye known as Yellow No. 5, which Young said he will permanently approve for use in foods.

Young said that, although Yellow No. 5 contains "carcinogenic constituents, an analysis of the risk associated with exposure to those constituents shows the risk to be so low that the agency can conclude that the product itself is safe."

Dr. Sidney M. Wolfe, director of the Health Research Group, said: "These carcinogenic dyes create a serious hazard to the public health. The agency's action is wholly indefensible because the dyes serve no useful purpose . . . .