A D.C. City Council committee approved a bill yesterday that would grant most of the concessions sought by the District's cable television contractor, including a provision allowing the company to seek additional changes in the franchise agreement if it encounters major financial problems.

However, Robert L. Johnson, president of District Cablevision Inc., the contractor, said he will not know if the committee's action is acceptable until he has discussed it with officials of Tele-Communications Inc. TCI, the Denver-based cable operator, has offered to put up $45 million in financing to build a cable system here.

The cable television committee voted 3 to 0, with two members absent, to approve the changes in the franchise to enable District Cablevision to secure the financing. But the committee added a series of amendments to give the council greater control in determining whether any future modifications should be granted.

In July the council approved emergency legislation that temporarily granted many concessions sought by District Cablevision.

The cable committee vote yesterday was the first step toward a final council action to end months of debate over modifications that would significantly reshape the system that District Cablevision, in bidding for the franchise, promised to build.

Some council members feared that the cable firm was trying to renege on a promise to wire the entire city. Others argued that the city should seek new franchise bids because the modifications, in effect, constitute a new agreement. In fact, the pending bill calls for transferring the franchise to a limited partnership, in which District Cablevision would have a 25 percent interest and TCI would have a 75 percent interest.

City Council member Betty Ann Kane (D-At Large), chairwoman of the cable committee, said that District Cablevision's submission earlier this week of a five-year construction schedule and its plan to use the modifications to secure $45 million in cash and loans are evidence of a legal commitment to wire the entire city.

"I don't think anybody is totally happy," said Kane. "I'm sure we've protected the public interest."

District Cablevision President Johnson said the council had "gone a very long way to add major concessions to make the system economically viable," but that he must confer with TCI officials before he can say whether the cable committee's amendments to strengthen the council's hand in future modifications of the franchise are "deal breakers."

The issue that has raised the most concern on both sides concerns future modifications due to extraordinary circumstances.

District Cablevision had sought to have the city's cable office empowered to grant temporary modifications in some instances without the council's approval. Johnson said having the council approve every change would be too time-consuming.

Kane, however,saying District Cablevision's proposal would have circumvented the council, insisted that the council exercise greater control over any changes. She succeeded in getting her committee to require the cable firm to demonstrate that future modifications are needed because of unforeseen "extraordinary circumstances" and to require council approval for all changes. The bill also requires the council to make certain that any future relief granted to the cable firm be "consistent with protection and furtherance of the public interest in cable television."

City Council member Wilhelmina Rolark (D-Ward 8) said the key to granting the modifications will be the council's ability to retain authority over what types of modifications should be granted. She said the council is wary of any attempt by the cable firm to avoid wiring certain sections of the city.

Under the modified cable agreement, some District homes would be wired for cable in 1986 and the system would be completed by 1990. As a result of the proposed modifications, the number of residential cable channels would be reduced from 78 to 54, the commitments for public and municipal programming would be limited to one-time grants of $500,000, and only a portion of the institutional cable network for use by businesses would be activated.