The District of Columbia's new automobile towing program was almost halted yesterday when the company that operates the tow trucks fired 19 employes in a labor dispute, D.C. Transportation Department officials reprted.

Late last night, a company official said the workers had agreed to report for duty this morning, "and if they do, we will let them work." If that happens, he said, negotiations of disputed issues will continue.

The firings followed two brief work stoppages this week by the truck drivers. Officials of Transportation Management Inc., the minority-owned tow truck firm, said the drivers were not satisfied with offers of higher pay that would have been coupled with a promise not to walk off the job during future disputes.

The drivers are not union members. Herbert Long, secretary of the truck frim, said he understood that the Teamsters Union was attempting to organize the workers. "We have no strong feelings about unionization," Long said.

Long said the workers had no individual spokesman.

Only five of the company's 25 trucks were on the streets yesterday, driven by supervisors and workers who syated on the job, according to James Hillman, the company's operations chief.

John Brophy, who heads the parking enforcement program for the city Transportation Department, said there were no reports that the lack of trucks to move cars parked in curbside lanes on major arterials was slowing rush-hour traffic yesterday.

Hillman said the workers are paid the minimum wage of $2.90 an hour plus an incentive bonus based upon the number of cars towed each day. That results in a base pay of $40.60 for a 12-hour day, Hillman said.