MCI Communications Corp. signed a $4.4 million, 20-year contract with Amtrak yesterday to build a fiber-optics communications system along the railway's Washington-New York right of way.

The venture will help the Washington-based telecommunications company quadruple its long-distance circuits in the Northeast corridor, giving MCI an edge over several other companies competing for the long-distance dollar.

Amtrak had planned to spend $9 million to build a D.C.-NYC communications system for its own uses. Now, as part of the agreement, MCI will provide the railroad with telecommunications services over the fiber-optic lines -- from Washington to Philadelphia by Jan. 1, 1984, and to New York by Dec. 31, 1984.

MCI currently relies on microwave transmissions to serve the Northeast and other sections of the country. The microwave system employs a series of relay stations, at 20- to 25-mile intervals, to link customers. MCI now has 10,000 working microwave circuits between Washington and New York.

Fiber-optic technology will give MCI an additional 40,000-circuit capacity to handle Washington-New York communications, the company's officials said yesterday, and the new system could be expanded to 120,000 circuits.

That kind of capacity is well worth the $4.4 million contract cost, MCI Chairman William G. McGowan said. "The incremental costs of adding capacity to a fiber-optic system is far more economical" than putting up more microwave towers, McGowan said.

A fiber-optic system transmits computer data and telephone conversations via pulses of infrared light. The light is generated by laser diodes and is carried along thin strands of silicon-coated, ultra-pure glass. The individual fibers are bundled into cables including as many as 44 fibers. Each cable has a diameter of about 7/8 inch.

Under its agreement with Amtrak, the federally subsidized passenger railroad, MCI will use the railroad's right-of-way to lay a fiber optic cable linking Washington to New York through Baltimore, Wilmington, Philadelphia, Trenton and Newark.

Other telephone companies already using fiber-optic links include American Telephone & Telegraph Co. and General Telephone and Electronic Corp. AT&T is building the longest line, linking Richmond to Boston.

MCI officials declined to give the overall cost of building its fiber-optics system, but said their costs, on a proportionate basis, would be lower than those incurred by AT&T.

"We can do the job cheaper because we aren't replacing anything, and AT&T is," said MCI spokesman Gary Tobin. "We aren't taking out old cables and putting in something new. We are putting in the state of the art, because we would have had to build anyway."