Sen. Ernest F. Hollings (D-S.C.) has introduced legislation that would fund major improvements to National and Dulles International airports, presenting what transportation officials say is a serious obstacle to plans to transfer control of the airports from the federal government to a regional authority.

A second potential snag for the Department of Transportation's plan may come from a major air carrier. A spokesman for American Airlines said yesterday that it is likely to press Congress next month to expand National's limits on nonstop flights in and out of National to 1,000 miles.

Countering those moves to oppose the plan, the airline industry gave Transportation Secretary Elizabeth Hanford Dole, the transfer bill's top proponent, good news this week when it said it is dropping its objections to that legislation and will support it without the reservations it had previously expressed.

The furious activity this week on the issue of who should control the airports is an indication that things are heating up in anticipation of hearings scheduled for mid-June in the Senate's Commerce, Science and Transportation Committee, where Hollings is the ranking Democrat.

"Our chances are not better than 50-50," said Rep. Frank Wolf (R-Va.), an early advocate of placing the airports under a local authority. "But we've come in recent weeks from a situation where we were one in 10. We've made a lot of progress."

Hollings, who introduced his bill Wednesday, appears to want to stop that progress. He said the federal government should continue to control the airports because they are the entry point to the nation's capital. The airports should not be "left to the whims of any state government," Hollings said in a letter yesterday to other senators. "Under this logic, the federal government should divest itself of Smithsonian museums, the Botanical Gardens and the National Zoo."

Hollings said the $46 million the regional authority would pay to lease the airports is too cheap, because the Grace Commission, a federal spending watchdog group, has estimated their worth at $342 million.

However, Hollings' bill would authorize the federal government to spend $250 million to update facilities at National Airport and build a new terminal at Dulles.

The DOT's transfer legislation, sponsored by Sen. John C. Danforth (R-Mo.) and Virginia's two senators, represents the most successful effort by any administration to divest itself of the two airports, the only two operated by the federal government. Administrations have been trying to get rid of the airports since the 1940s, but opposition by the airline industry, and congressional desire to retain control, have crippled past attempts.

The bill, which would set up a local airport authority with directors from Maryland, Virginia and the District of Columbia and one named by the president, comes on the recommendation of a federal commission headed by former Virginia governor Linwood Holton.

One of the main reasons the DOT wants to transfer the airports is to allow for the facilities recommended by Hollings' bill. In the past, the Treasury's general fund has paid for such capital improvements at the two airports, and deficit prob- lems have prevented any expenditure. A local authority would be able to float bonds to pay for the construction.

All sides agree that National desperately needs new parking lots, roadways and terminal facilities, and that Dulles will not become a major airport until it has a new terminal to accommodate an airline "hub" operation.

Hollings, by recommending that the government pay for the improvements, essentially makes the transfer idea moot, transfer proponents said.

Hollings said the $250 million would come from the Federal Aviation Administration's aviation trust fund, paid for by a tax on passenger tickets and airline fuel. The $7 billion trust fund has the money, but disbursing the $250 million would add to the federal deficit, and congressional staff members said passage of Hollings' bill is doubtful.

Even so, his measure could prompt fatal doubts about the transfer bill, Wolf said.

Several airline industry and Capitol Hill sources said yesterday that they were puzzled by Hollings' action because he had shown little previous interest in the airports. Several said they understood that Hollings is doing a favor for Sen. Paul S. Sarbanes (D-Md.), who is opposed to the transfer. But Mike Fernandez, Hollings' spokesman, said, "There was no deal." Sarbanes could not be reached for comment last night.

Sarbanes and other Maryland officials are against the transfer because spurring growth at Dulles threatens growth at the Maryland-owned Baltimore-Washington International Airport, and because Maryland would have only two seats on the 11-seat regional authority.

Another possible problem for the transfer bill is the effort by American Airlines to expand the 1,000-mile perimeter rule. American has tried for years to have the rule changed. Because of the rule, American is the only airline unable make nonstop trips between its main "hub" airport, Dallas-Fort Worth, and National.

If the perimeter rule is lifted, airlines would divert many National flights to Texas and end service to some other cities. This would cause congressmen from those areas to oppose the transfer bill, Wolf said.

"If American Airlines gets the perimeter moved, it will kill this bill," Wolf said. "You're going to bump flights from Louisville, Akron and Toledo, wherever."

Gene Overbeck, American's senior vice president for government affairs, said he does not think that extending the perimeter would lower service to other cities.