Mayor Marion Barry urged the City Council yesterday to approve a dozen major concessions to undercapitalized District Cablevision Inc., including scaling back the proposed cable television system here and delaying payments the firm must make to the city.

Barry said the changes in the District's franchise agreement with the firm were needed to make the planned cable system financially feasible. But he reasserted his administration's commitment to making the system available to all residents throughout the city.

In a letter to the City Council, Barry's top cable television official, Richard Maulsby, recommended a series of changes in the franchise agreement that the mayor endorses, including: A reduction in the number of channels available, from 78 to 54. Deregulation of rates charged cable customers, paving the way for the higher basic rate District Cablevision had asked for. A construction schedule extended from four years to five that calls for wiring first at the boundaries of the District and then gradually moving toward the central downtown area. The contractor would not have to wire buildings already equipped with satellite dishes or other alternative technologies. A restructuring of the security fund that serves as collateral against a default by the firm, reducing the amount required to be in the fund from $2 million to $500,000. Elimination of a two-way institutional network to be used for data processing among businesses and government agencies.

Other proposed concessions range from changes in how the gross revenues are calculated for tax purposes to reducing funding for public access programming.

"Because of the experiences of other cities and the economic realities faced by DCI in seeking financing, I am willing to support certain changes if it means that construction can go forward with our cable system," Barry said. "We must not permit changes, however, which would deny access to cable to any part of the District . . . . "

Robert L. Johnson, president of District Cablevision, said he was pleased with the administration's response to his request. Last week, company officials announced that changes in the agreement with the city signed last February were needed because of economic factors and their inability to raise financing for the proposed system.

"I think the mayor is being extremely helpful in understanding our economic problem," Johnson said.

Council approval of the changes likely would pave the way for greater involvement in the cable project by Tele-Communications Inc., a Denver-based cable giant that last week offered up to $30 million in financing to bail out District Cablevision. TCI owns 20 percent of District Cablevision and has a contract to manage the system.

Barry, in his monthly press conference Wednesday, warned that District Cablevision's difficulties attracting investment could lead to outside groups wresting control of the city's cable system.

Johnson discounted such a possibility and said, "I think local control is strengthened under the agreement."

Council member John A. Wilson (D-Ward 2) said the city should start over in awarding the contract. "I don't think starting all over is going backwards," Wilson said. "It says you made a mistake. I don't think they DCI can do it."

Betty Ann Kane (D-At Large), the chairman of the cable television committee, said she was happy that Barry did not back away from his commitment to so-called "universal wiring" that would make cable television available to residents throughout the city.

Kane's committee will conduct a hearing July 2 before taking action.