The Justice Department said yesterday it has reached an agreement with Allied Corp. that will allow Allied to acquire 20 percent of The Signal Cos. Inc.

Allied has agreed to sell its air turbine starter business to settle an antitrust suit the department plans to file challenging the proposed merger.

The department said it plans to file a consent decree in U.S. District Court here, along with a complaint alleging that the merger of the two companies would reduce competition in the air turbine starter business.

The merger, as originally proposed, would violate federal antitrust laws by eliminating competition between the two largest manufacturers of air turbine starters, said Charles F. Rule, acting assistant attorney general in charge of antitrust.

Signal's Garret Pneumatic Systems Division has long been the leading producer of air turbine starters, and Allied's Bendix Fluid Power Division is the second largest, the department said. Together, the two firms accounted for more than 70 percent of all air turbine starter sales in 1984.

Annual sales of the machines total about $40 million in the United States and $50 million in the non-communist world, the department said.

Under terms of the agreement, the department will not block the merger, which is due to proceed next week, and Allied will try to sell its air turbine starter business by the end of this year.

If Allied does not find a buyer by then, it must sell its entire Bendix Fluid Power Division by March 31, 1986.

Allied, based in Morris Township, N.J., is a diversified producer of chemicals and automotive, aerospace and industrial products. Allied reported 1984 net income of $488 million on sales of $10.7 billion.

Signal, based in La Jolla, Calif., operates aerospace, chemical, automotive and energy businesses. Signal made a profit of $285 million on sales of $6 billiion in 1984.