The Federal Aviation Administration, which has requested an $80 million supplemental appropriation to avoid furloughs for air traffic controllers, safety inspectors and other employes, has told its parent Transportation Department that it needs another $50 million.

The request, a surprise to department officials and FAA advocates on Capitol Hill, came amid increasing congressional concern that the agency is stretched too thin to meet the growing traffic and safety demands of the deregulated airline industry.

The issue is under discussion in the department. "Nothing has been decided on any of that yet," FAA spokesman Stephen D. Hayes said.

Rep. Norman Y. Mineta (D-Calif.), chairman of the House Public Works and Transportation subcommittee on aviation, made the issue public yesterday in testimonybefore Rep. William Lehman (D-Fla.), chairman of the Appropriations subcommittee on transportation.

Mineta said "it would appear that neither DOT nor FAA have a budget system that is able to either monitor . . . spending or to control their expenditures."

Mineta cited increased costs of air traffic control communications links and of relocating employes as part of a long-time FAA goal to consolidate flight-plan filing and weather-information services for aviators.

The need for more controllers and inspectors has been established at the Office of Management and Budget. Last September, Transportation Secretary Elizabeth Hanford Dole announced that 1,000 new controllers would be hired by the end of fiscal 1987.

A goal of 500 new hires was set for the current fiscal year, which began last Oct. 1. By the end of March, the total increase in controller strength was 28, according to congressional and FAA sources.

"We believe we will meet the target of 14,480 controllers by the end of September," Hayes said.

He said that attrition and retirements have resulted in a growth rate smaller than anticipated but that controllers on duty are rapidly gaining experience as the FAA recovers from President Reagan's 1981 firing of 11,400 illegally striking controllers.

FAA officials have expressed concern since Congress passed the Gramm-Rudman-Hollings balanced-budget act that they would have to furlough employes to meet this year's budget.

The FAA lost $116 million from its $2.7 billion budget as its share of Gramm-Rudman-Hollings cuts. Dole has said controllers and safety inspectors will not be furloughed.