The Federal Communications Commission yesterday agreed to study the controversial issue of whether the nation's telephone companies should be permitted to operate cable television systems.

At the same time, the commission went a step further in a related matter and formally proposed that small telephone companies be permitted to compete in their service areas for rural cable television service.

FCC member Joseph Fogarty said it is time to consider whether existing commission rules "impose too great a burden on today's consumers in terms of foregoing cable service which can be provided now by telephone companies."

Although broader inquiry is merely a preliminary step, the question is likely to foster a barrage of criticism from the cable television industry, since lifting FCC rules on cross-ownership could open the cable industry to competition from phone companies, which already have wires in most homes.

Although American Telephone & Telegraph has said consistently that it is not interested in getting into the cable television field, other phone companies, particularly rural firms, have suggested that with a lifting of FCC cross-ownership rules, they would be interested in offering some of those services. FCC rules bar telephone companies from the cable field in their own service areas.

Cable operators historically have been highly critical of any proposals that would enable phone companies, which already have hook-ups with residences, to take advantage of that situation in launching cable television systems.

In fact, Brenda Fox, counsel for the National Cable Television Association, called the inquiry a "wasteful" use of industry legal resources and said the association would remind the FCC of a series of conflicts between the two industries over cable access to telephone poles. As a result of those flaps in the early 1970s, legislation was adopted stating the ground rules for telephone company and cable television dealings.

"You shouldn't have the only line on the street going to the same guy," Fox said. "There is a need for diversity and competition there."

But FCC Chairman Charles Ferris called the inquiry and related preliminary decision part of the commission's "open entry" policies. Ferris said he agreed that the time had come to re-evaluate FCC cross-ownership rules barring telephone companies from providing cable services.

"The cable industry has obviously undergone major changes in the past 10 years and is well on its way to becoming a strong and established player in the overall communications industry," Ferris said. "No policy of the commission should become so imbedded that it is not worth a second look."

The commission's formal proposal would revise a 30-homes-per-mile standard in rural areas enabling telephone companies, with only limited FCC oversight, to enter in a small way the cable television business.