The Justice Department asked a federal court yesterday to drop a four-year-old antitrust case against Bethesda-based Martin Marietta Aluminum Inc., in return for the company's promise to refrain from fixing prices on its titanium bar and billet products.

In a related development, the department also agreed to dismiss a civil damage suit against the company in exchange for an undisclosed fine levied against Martin Marietta Aluminum. The damage suit was brought to recover losses stemming from an alleged price-fixing conspiracy that originally involved five companies.

The agreements were included in a proposed consent decree filed by the department yesterday in U.S. District Court in Pittsburgh. Under the terms of the decree, Martin Marietta Aluminum, a subsidiary of Martin Marietta Corp., agreed to:

* Refrain from fixing or conspiring to fix prices, and from exchanging any price information with competing titanium and billet producers;

* Establish an antitrust monitoring program to be in effect each year of the 10 years that the decree is in effect;

Furnish a copy of the decree to its officers and other employes responsible for setting titanium prices;

* Collect written acknowledgements from its officers, saying they understand the nature of the decree and the penalties for violating it.

Titanium is used primarily in aerospace construction and has basic defense industry applications. The suit alleging price-fixing was brought by the government on Sept. 28, 1978. The other defendants included RMI Co. of Niles, Ohio; Crucible Inc. of Robinson Township, Pa.; Lawrence Aviation Industries Inc. of Port Jefferson Station, N.Y., and Titanium Metals Corp. of America, of Pittsburgh.

Marietta was the last of the defendants to settle.