District Cablevision, Inc. has agreed to pay the Chesapeake & Potomac Telephone Co. $55.6 million to construct the District's proposed cable television network, under an agreement made public yesterday by city officials.

The 15-year agreement was described as a key step toward building the proposed 79-channel system for city residents. Under the agreement, some homes would be wired for cable by 1986 and the entire system would be completed within five years.

"It's a very straightforward agreement. There are no surprises," said Richard Maulsby, executive director of the city's cable television office. "It should reassure the people in the D.C. City Council."

Some City Council members and other officials previously had expressed concern about C&P's involvement in the cable project, warning that it might lead to reduced competition in some areas of communications.

Maulsby and other officials said yesterday that the costs cited in the agreement were in line with earlier estimates. In addition, they said, the agreement includes provisions prohibiting C&P from restricting competition.

The agreement "provides significant guarantees that there will be competition between DCI and C&P," said District Cablevision President Robert L. Johnson. "C&P will build us a quality system."

The City Council's public services and cable television committee is scheduled to hold a hearing next Tuesday on a proposed agreement granting District Cablevision a franchise to set up the cable system. The new agreement between District Cablevison and C&P for construction of the transport lines is designed to help carry out the franchise proposal.

A spokesman for City Council member Betty Ann Kane (D-At-Large), who heads the public services committee, said that the cable firm's agreement with C&P was being reviewed and that Kane would have no immediate comment on it.

C&P also is required to obtain approval from the Federal Communications Commission to construct the proposed cable system. An FCC spokesman said the issue is under "active consideration." Objections have been filed by firms that sought unsuccessfully to win the city franchise, the spokesman added.

A C&P spokesman said yesterday that telephone users will not face any increased charges because of the proposed cable venture. The agreement ensures that any costs resulting from the project "will be taken out of profits" and will not be included in phone rates, the spokesman said.

The City Council is expected to take final action on the cable proposal shortly before Christmas, officials said. The franchise agreement would then be signed by Mayor Marion Barry, who has already described it as "fair and beneficial." Construction is expected to start next year.

Concern over competition has centered on proposals to use the cable network for business ventures other than televised entertainment. These are expected to include transmission of data among government agencies, businesses and other organizations. For example, a bank could use the network to exchange financial data with branch offices and customers, officials said. Officials said competition would be preserved under a provision that states: "Neither DCI nor C&P shall be restricted in their right to compete in the offering of services . . . . C&P recognizes that DCI may be competing directly with C&P in the provision of services."

The 117-page agreement also provides for possible penalties of $1,000 to $5,000 a day against C&P for any unwarranted delays in construction.