The Consumer Product Safety Commission yesterday declared that three household products containing cancer-causing asbestos are a hazard to the public. Commission members could not agree on how to ban their sale, thus allowing the goods to remain available until further action.

The commission also directed its staff to begin work on determining the extent and nature of asbestos in consumer products, a step that could lead to a general ban on its use.

The commission action comes 20 months after published findings that some plaster patching, or spackling, compounds contain high levels of asbestos, and 18 months after a citizen reported that artificial fireplace ashes containing asbestos were being sold.

Both were called hazards yesterday by the commission, as way any tremolitic talc containing asbestos. The talc is used in putties and spackling compounds.

All three substances were brought before the commission for action by citizens or outside groups, despite an April, 1976, commission staff memo calling for immediate action toward a sweeping ban on many asbestos-containing consumer goods.

Asbestos also is used in some children's modeling clay, papier mache, texturized paints, vinyl asbestos and asphalt asbestos flooring, flooring backings and adhesives, and wallboards, among other goods. Its presence in a product may vary from brand to brand.

With one member absent, the commission split 2 to 2 on how to end the sale of yesterday's three products. Two commissioners, David Pittle and Thaddeus Garrett, favored a quick ban under the Hazardous Substances Act with provisions for dealers to repurchase goods from consumers.

Chairman S. Hohn Byington and Commissioner Barbara Franklin favored action under the Consumer Product Safety Act, a more time-consuming process -- taking perhaps months -- that they said would better withstand legal challenges.

The commission's ruling on the decorative fireplace ash represented something of a triumph for a Washington women, Rachel Scott. She had petitioned the commission on Nov. 14, 1975, for action against the goods, but the agency's staff declared her typewritten letter not legally a petition for action.

The commission reversed that on Wednesday and yesterday the ashes were declared hazardous.

The artificial ash used in gas-burning fireplaces can be removed, experts said, but care should be taken not to stir it up. Dr. Robert Sawyer of Yale University recommends wetting the ash with a mixture of water and detergent; a sprayer or mister can be used to apply it. Allow it to sit for a while and then scoop it into a plastic bag, close the bag and put it out with other trash.

Spackling compound already applied should be left alone -- do not sand or disturb it, Sawyer said. Painting can help to reduce asbestos exposure.