The Federal Aviation Administration's ambitious modernization of its air traffic control system will cost billions of dollars more than the agency estimates because of unforeseen technical problems and delays, a congressional report says.

Largely because of unexpected problems in developing and installing the new communications, radar, weather observation and computer systems, the upgrading will cost at least $24 billion, the General Accounting Office told Congress Tuesday.The FAA, which operates the air traffic control system and is obtaining the new equipment, acknowledges that the program has fallen behind schedule but has put the expected cost at $15.3 billion.

"Many of these technologies had to be invented, and the FAA underestimated how long it would take to invent some of these things," Kenneth M. Mead, an associate director of GAO, told the House transportation appropriations subcommittee.

The report by GAO, Congress' investigative arm, also said hundreds of pieces of equipment that are being delivered to FAA facilities across the country are simply sitting in sheds because the agency lacks enough workers to install them.

"It's like ordering a piano and not having a living room to put it in," said Rep. William Lehman, D-Fla., chairman of the subcommittee.

FAA Administrator Allan McArtor said in an interview after the hearing that the GAO figures were "misleading," but acknowledged that the plan, introduced in 1981, is running behind its original timetable.

The GAO report focused on the National Airspace System plan, the second largest civilian technology project ever undertaken in the United States, behind only the Apollo manned spacecraft program.

Federal officials believe the new equipment is necessary to keep up with the continuing growth of aviation, the fastest growing segment of American transportation.

The FAA originally hoped the new equipment would be in place by 1996. But officials now concede that because of delays, the project will not be completed until at least the year 2000.

The study by GAO said that of the 12 major systems that comprise the modernization project, only one a computer is nearing completion. Major components have been delayed from between one year and five years, the report said.

Reagan administration officials have blamed many of the delays on the slowness of federal purchasing procedures, and on a refusal by Congress to provide enough money to buy the equipment.

Meanwhile, a broad coalition of aviation groups, aircraft manufacturers and airlines called on not only the industry but air travelers to put pressure on the government to expand airspace and airport capacity.

The coalition, forming a group called Partnership for Improved Air Travel, announced a two-year campaign to enlist grassroots support for spending more money on airports and improvements in the air traffic control system.

The air traffic modernization plan must be put "on a fast track" and new airports must be built or air travelers will face declining service, mounting delays and travel problems in the coming years, the coalition warned at a news conference.

"Unless we modernize the (air traffic system) quickly, we'll choke off growth to the detriment of all," declared Robert Crandall, chairman of American Airlines.

Crandall was among five airline chief executives, and leaders of groups representing aircraft manufacturers, business flyers, private and commercial pilots and airport officials who attended a news conference announcing the campaign.

The group envisions spending up to $15 million over the next two years to publicize the need for more airports and an improved air traffic control system.

"The nation has not yet made a commitment to create an (aviation) system that can efficiently meet today's demand and anticipate tomorrow's," said Herbert Kelleher, the chairman of Southwest Airlines.