Yesterday's Washington Post incorrectly quoted Federal Aviation administrator J. Lynn Helms' estimates of the cost of a proposed modernization of the air traffic control system. Helms predicted that the 20-year program in its first 10 years would cost $8.7 billion to $9 billion, which he said would constitute the bulk of the plan's capital spending.

Federal Aviation Administration chief J. Lynn Helms, saying he had the support of President Reagan, yesterday called for major new taxes on airline tickets and aviation fuel to pay for a proposed $9 billion, 20-year retooling of the nation's air traffic control system.

Helms said the administration would ask Congress to raise the 5 percent tax on airline tickets to 8 percent, levy a 14-cent-per-gallon tax on currently tax-free jet fuel and raise the tax on the fuel piston-driven planes use from 4 1/2 cents a gallon to 12 cents.

The fuel taxes would rise a further two cents a gallon for each of the next five years under the plan.

The Air Transportation Association of America, which represents the major airlines, withheld immediate comment on the proposal. However, it seems certain to generate controversy in the aviation industry, which is already hard-hit by the recession.

If enacted by Congress, the new rates would generate about $3.4 billion annually, Helms said, more than enough to pay for the modernization plan, which was unveiled yesterday before a gathering of aviation industry representatives at FAA headquarters.

The program would replace the IBM computers, which date from the 1960s, with standardized, higher-capacity models, automate many air traffic controller jobs and reduce the work force by about one-third from levels before last August's strike. Over the next 20 years, Helms estimated, it would save $25 billion in operating and maintenance and fuel costs that would result if the current system were retained.

The modernization plan would cost between $8.7 billion and $9 billion, Helms said. In size, it would probably rank second only to the Apollo space program among nonmilitary federal programs, according to Helms.

"I have discussed it personally with the president," Helms said of the plan. "The president strongly supports it. I anticipate no problem within the administration." The president's Office of Management and Budget, he said, had approved it on condition that the new taxes cover the costs in full.

In general, large commercial aircraft are taxed on the ticket while private planes and smaller commercial planes pay tax on fuel, an FAA spokesman said. A Department of Transportation spokesman said no decision had been made if the new tax would be applied the same way. But he noted that tax increases proposed last year by the Reagan administration would have followed the same system.

Helms had been under a congressional deadline to devise a comprehensive strategy for coping with growth in air traffic, which is projected to rise from 134 million flights in 1980 to 290 million in the year 2000.

Outlined in a 450-page document released yesterday, the plan calls for the "highest practical level" of automation. Consoles that now require three controllers would be worked by two or possibly one controller, Helms said.

Many messages that now go to pilots by voice would be conveyed in electronic form and appear on cathode ray screens in cockpits.

The 200 "en route" control centers and airport approach radar rooms would be consolidated into about 60 facilities. About 1,200 of 3,000 radar, beacon and radio installations on the ground would be eliminated as more modern equipment was installed.

The more than 300 flight service stations, which process flight plans and provide weather reports, would be absorbed into about 60 automated facilities. Pilots would be able to call the stations' computers directly and get readouts on cockpit screens of weather and other flight data.

Beginning in the next decade, new software would allow the computers to select the most fuel-efficient flight path for a given flight, reducing the wastful diversions that planes fly when human controllers see potential conflicts at the last minute.