Officials of Amkrak proposed yesterday that the government contract with it to operate the nation's intercity passenger rail system at a specified cost.

Such a "contract," outlining the basic system Congress wants operated and the funds it is willing to spend on it, would provide the stability necessary to make capital improvement commitments and would provide clear efficiency incentives to Amtrak, its officials said yesterday.

The contract proposal was contained in a 12-page "statement of mission" said to be the work of Amtrak's new president, Alan Boyd, and a board of directors recently reconstituted as a result of some appointments by the Carter administration.

The statement cited what it called "some persistent and major obstacles" to the success of the Amtrak venture, including the inheritance of old, obsolete and poorly maintained passenger equipment, poor track, lack of a computer system, difficulty in attracting qualified personnel because of compensation limits, and the inability of the company to contol efficiency and productivity because of its contractual relationships with other railroads.

The problems are exacerbated when Amtrak doesn't know each year how much subsidy it will get from Congress, Boyd said at a press conference yesterday, "If you're living from hand to mouth, it's very difficult to plan," he said.

Boyd said a five-year advance funding program would seem "reasonable" to him and that he would propose spending $200 million a year on capital improvements during that time.

Donald P. Jacobs, chairman of Amtrak's board of directors, told the news conference the heart of the problem came with the genesis of Amtrak in 1970, when it was believed that efficiently run intercity passenger service could be profitable.

"I don't think it can," he said yesterday, adding that no other intercity passenger service in the world makes a profit.

"Since profitable service is an improssibility and there is still a need . . . it seems to us that a decision on the size of the rail system and the amount of money to be spent ought to be made by Congress," he said.

For the current fiscal year, Congress has authorized more than a half billion dollars in subsidy payments for Amtrak.

The board rejected the possbility that the U.S. intercity passenger rail system would perish completely, suggesting intstead that it was more likely that Amtrak would be nationalized if it was unable to improve on existing operations.

But the board warned that nationalization would be no panacea. "There is no reason to feel that another layer of bureaucracy would operate the system any more efficiently," Jacobs said, adding it probably would be less so.

Boyd said he had not discussed the board's recommendation with members of Congress or the administration yet. The administration is working on a final plan for drastically reducing Amtrak service in order to keep its rising deficit in check.

In a related development, Amtrak directors yesterday approved a contract with Southern Railway for Amtrak to take over operation of the Southern Crescent passenger service effective Feb. 1. The Crescent operates daily between Washington and Atlanta and on three days each week extends to New Orleans. CAPTION: Picture, Amtrak President Alan Boyd fields a question during a briefing yesterday as Chairman Donald Jacobs looks on. By James M. Thresher-The Washington Post