The Federal Aviation Administration yesterday banned proposed nonstop flights from National Airport to many distant points, blocking widely promoted plans by three major airlines in inaugurate service next week to Dallas, Houston and other cities.

The action is designed to halt plans, announced earlier this month by Braniff, American Airlines and Pan American World Airways, to ignore a 14-year-old voluntary agreement with the FAA that prohibited nonstop service from National to most cities more than 650 miles away from Washington.

That would have meant diverting many flights and thousands of passengers to crowded National Airport and away from underused Dulles International Airport. Both airports are government-owned.

Yesterday's decision comes at a time when Transportation Secretary Drew Lewis is reviewing a permanent operating policy for both National and Dulles. The day after the airlines announced plans to flout the so called perimeter rule, Lewis called their decision "inappropriate and unacceptable" and told the FAA to make the rule mandatory.

Although some key Reagan administration officials are known to favor minimal regulation of the airlines, including possible abolition of the perimeter rule, Lewis has been eager to preserve the status quo while formulating a final airport plan.

The manadtory rule already has come under attack by American, which recently filed a lawsuit in New Orleans seeking to block the FAA from enforcing the voluntary rule. The court is expected to rule this week. An American spokesman in Houston yesterday declined further comment.

A Pan Am Spokesman said yesterday that airline will obey the new FAA rule.

Raymond Chanaud of Braniff said the airline is "studying the situation." Braniff had planned to pull all its domestic flights from Dulles beginning next Monday and institute five nonstop round-trip flights per day from National to Dallas-Fort Worth and one to Tulsa.

Existing service to seven cities located beyond the permeter remains unaffected by yesterday's action. Those cities are Miami, Tampa, Orlando, West Palm Beach, Minneapolis, Memphis and St. Louis.

The FAA has been under intense pressure for years from Northern Virginia residents to move noisy flights from close-in National to remote Dulles, an action ardently opposed by some congressmen because of National's proximity to Capitol Hill.

But some local officials, particularly those in Fairfax County who have long sought to beef up use of Dulles, were jubilant at yesterday's announcement.

"That's fantastic, just fantastic," said John F. Herrity, chairman of the Fairfax County Board of Supervisors. "They [the FAA] bagged those greedy characters. The problem with the airlines is that they're looking at this year's balance sheet, not the future of aviation in this area which is Dulles airport."

"I'm very pleased," said Rep. Frank Wolf, a Northern Virginia Republican, who had said the use of National for the longer flights would ring a death knell for Dulles.

If the flights from National had been allowed, other airlines said they were considering flights from there to Fort Lauderdale, New Orleans, Kansas City and possibly Denver. National's runways are too short for the larger passenger jets capable of flying nonstop to the West Coast.

FAA officials said airlines and their employees who violate the rule, which is effective immediately, are subject to a variety of civil and criminal penalties, including fines and possible disciplinary action against pilots that could mean the loss of their licenses.

"We would certainly hope the airlines would go ahead and live with this," said Jim Wilding, director of Metropolitan Washington Airports. "I certainly hope they'll comply."

In its 21-page order signed by FAA administrator J. Lynn Helms, the agency reserved its sharpest comment for Pan Am, which has taken out full-page newspaper advertisements promoting its new service planned to start June 18.

Said the FAA: "If, in fact, the public is invonvenienced, it will be by Pan American's precipitous actions, not the [FAA's]."