The Department of Energy yesterday approved a conditional $250 million loan guarantee to permit the start of construction on the nation's first major synthetic fuels plant.

The loan would finance part of the first-year construction costs for the Great Plains Coal Gasification Plant near Beulah, N.D. The project is designed to produce 137 million cubic feet of synthetic gas a day by 1984 from nearby lignite coal deposits for sale by five pipeline companies.

Approval of the federal loan guarantee apparently overcomes a legal dispute that had threatened to delay a start of construction at least until next year.

meanwhile, negotiations between the United States and Canada over the first phase of the Alaskan natural gas pipeline project were concluded successfully yesterday.

Canada announced it would approve construction of the initial, "prebuilt" segment, which is to deliver natural gas from Canada's Alberta Province to the U.S. West Coast this November and to the U.S. Midwest by November 1981.

Canada had balked at beginning construction of the first segment until it received firmer assurances from the United States that the entire $20 billion project will be built.From the bottom segment in Alberta, a new line must be built through Canada to the Alaskan border connecting with the final section through Alaska to the large North Slope gas reserves.

The concern in Canada was that the middle segment would be built but that the more difficult, costly section through Alaska would fall behind schedule, leaving Canada with an expensive pipeline system through which no gas could flow.

President Carter assured Canadian Prime Minister Pierre Trudeau in a letter yesterday that, should such a delay occur, the United States would cover any Canadian financial losses. If necessary, the Carter administration will ask Congress to approve legislation making the project's future customers in this country liable for such costs, administration officials said.

The Senate and House recently passed resolution of support for the pipeline project to reassure Canada, and in his letter to Trudeau Carter added:

"I am able to state with confidence that the U.S. government now is satisfied that the entire Alaska Natural Gas Transportation System will be completed," Carter said.

The western leg of the project, running from Alberta into Oregon and California, is scheduled to deliver 240 million cubic feet a day this November. The eastern leg running through the Dakotas and Minnesota to Chicago is supposed to deliver 800 million cubic feet daily in November 1981. cTogether, these segments would replace about 200,000 barrels a day of foreign oil, the president said, making the United States less dependent on imports.

The full project is expected to carry 2.4 billion cubic feet of Alaskan gas daily to U.S. customers, replacing 400,000 barrels a day of foreign oil. The United States this year has imported an average of 5.8 million barrels a day.

The Great Plains Coal Gasification Plant, although producing a relatively small amount of gas, will be symbolically important as the first completed with help from the government's new synthetic fuels program, administration officials said.

The pipeline companies sponsoring the gasification plant have had difficulty obtaining full financing for the $1.4 billion project. The Federal Energy Regulatory Commission had ruled that the pipeline companies could recover the project's costs from their currect customers if it failed. But General Motors Corp., an important customer of one of the pipelines, sued to upset the FERC decision.