A public advocacy group yesterday asked the Food and Drug Administration to remove 10 commonly used dyes from the market, because animal studies have shown that all of them can cause cancer.

The dyes include one red and two yellow food colorings used mostly in candy, desserts and soft drinks. The other dyes, six red and one orange, are most often used in drugs and cosmetics, coloring everything from vitamin pills and cough syrup to lipstick and makeup.

The Public Citizen Health Research Group, founded by consumer advocate Ralph Nader, said it would sue the FDA if the dyes are not immediately banned. The FDA has included the dyes on its "provisional" list of potentially dangerous dyes, and the health group accused the FDA of bowing to lobbying pressure from the food, drug and cosmetic industries by delaying its final decision.

In a letter to FDA Commissioner Dr. Frank D. Young, the group said: "By failing to immediately ban these dyes, the Reagan administration is making a mockery out of its alleged cancer reduction goals and is completely demoralizing dozens of FDA employes who know these dyes are too dangerous for continuous use by the public."

An FDA spokesman, Emil Corwin, yesterday confirmed that the deputy commissioner, Dr. Mark Novitch, recommended in March that six of the dyes be banned as unsafe. "But that was only a recommendation," Corwin said, adding that Health and Human Services Secretary Margaret M. Heckler has the final decision.

The dyes' provisional status was to have expired Dec. 3, but was extended until February. Corwin said the FDA commissioner "needed a little more time."

To support its claim that FDA officials supported the ban, the health group released copies of an internal FDA memo written last month by Dr. Sanford A. Miller, director of the FDA's Center for Food Safety and Applied Nutrition.

Miller wrote to the commissioner that "we have already extended the provisional list so many times for such tenuous reasons that we are in danger of losing both a lawsuit and our credibility as a regulatory agency."

The FDA spokesman confirmed that Miller wrote the memo.

To support its accusation of heavy lobbying, the Nader group released a copy of a May letter to Heckler, signed by eight U.S. senators, urging that Red No. 3 not be banned.

The dyes on the provisional list are food colorings Red No. 3 and Yellow No. 5, found to cause thyroid tumors and chromosomal damage in animals, and Yellow No. 6, found to cause kidney tumors and allergies in animals. Those are three of only seven food dyes still marketed and account for more than half of the food coloring consumed last year.

Also on the list are Red Nos. 8, 9, 19, 33, 36 and 37 and Orange No. 17. All those dyes are used in various drugs and cosmetics and have been found to cause tumors in animals.