Federal Aviation Administrator Donald D. Engen, in an attempt to meet a budget cut, yesterday froze contracting, travel and hiring of employes other than air traffic controllers, safety inspectors and security personnel.

In a message to FAA employes, Engen called his action stringent and said, "While we will attempt to avoid doing so, reductions-in-force and furloughs are possibilities . . . ."

Top FAA officials worked through the holidays to determine what they would have to trim from the current FAA budget, set by Congress at $4.9 billion just before holiday recess. That is $55 million less than requested.

Engen and others have expressed greater concern about the potential additional impact of Gramm-Rudman-Hollings budget-balancing cuts. FAA officials said they are assuming that they will be told to absorb a further 5 percent cut for the current fiscal year.

"It appears that the FAA will not know exactly what its 1986 budget will be until early March. That will leave us less than seven months to accommodate the reductions. Therefore, it is prudent to begin spending cutbacks immediately," Engen said.

Engen and his boss, Transportation Secretary Elizabeth Hanford Dole, have said often that no cuts will be made in sensitive safety areas: controllers, inspectors and security forces.

But personnel costs are the major part of the FAA budget. The FAA has about 45,000 people, with 25,000 in air traffic control. About 14,000 of them actually work as controllers and the others as administrative and support personnel.

Most of the rest of the agency is devoted to oversight of airlines and aircraft and engine manufacturing and maintenance.

"It would be fair to say that the second-level stuff, the backup and the support, are going to be deferred," one FAA official said. Another said that "if Gramm-Rudman goes through as proposed now, you're talking a major change in the character of this agency."

The nation's airlines, which have been trying to grow faster than the air traffic control system will let them, were sounding alarms about this before Congress left town and repeated them yesterday.

Air Transport Association spokesman Daniel Z. Henkin said, "We are deeply concerned about cutbacks in FAA programs, particularly when there is a $3 billion surplus in the aviation trust fund."

The trust fund, financed primarily by an 8 percent tax on passenger tickets, has accumulated a $3 billion surplus. Its revenues can be spent only for aviation, but the administration and Congress have chosen to let the surplus build because spending it would increase budget outlays.

An attempt in the House late last year to take aviation trust fund expenditures off the budget failed narrowly. But Nancy Landon Kassebaum (R-Kan.), chairman of the Senate aviation subcommittee, has introduced legislation to exempt trust-fund expenditures from the Gramm-Rudman process.