The Senate approved a compromise bill yesterday that allows the federal government to lease National and Dulles International airports to a regional authority, a measure that proponents said will assure major improvements at both facilities.

Although the Senate rejected the Reagan administration's plan to sell the two airports, supporters said they were satisfied with the bill because the authority would remove the airports from direct federal control. The bill, which passed by a vote of 62 to 28, goes to the House, where it faces a tough battle.

"It has a 50-50 chance," said one supporter in the House.

Transportation Secretary Elizabeth Hanford Dole said that she was pleased with the Senate vote.

"I'm elated," said Dole, who has fought hard for the transfer.

"This is a compromise, but a major victory for the Reagan administration," said Sen. John W. Warner (R-Va.).

The bill would let a regional airport authority replace the Federal Aviation Administration as operator of the two Northern Virginia airports. The authority could issue bonds to raise money for improvements such as new terminals, parking facilities and roads.

Virginia officials fought hard for the bill, saying that hundreds of millions of dollars are needed for the airports and that the federal government is unwilling to appropriate the funds. Maryland officials protested that the plan would hurt the state-owned Baltimore-Washington International, which competes with Dulles.

Under the bill approved by the Senate, the government would lease National and Dulles to the regional authority for 50 years for $47 million. During that time, the federal government could propose selling the airports, but Congress would have to approve the transaction.

The administration had sought approval for a 35-year lease, after which the regional authority would own the airports. Several senators questioned whether the administration's sale price of $47 million was too low. Proponents, surprised by the widespread skepticism in the Senate, backed down.

Virginia's two senators, who led the fight for the bill, also agreed to increase the federal influence on the regional authority, adding two more presidential appointees to the governing body. This was a move to head off opposition by senators who felt that the authority was heavily weighted in favor of Virginia.

Sen. Paul S. Sarbanes (D-Md.), who led the opposition to the bill, said he believed the prolonged debate and 23 amendments revealed fundamental flaws in the legislation.

"I think this bill is in trouble in the House," he said after the vote.

But Sen. Paul S. Trible (R-Va.), who managed the bill, said: "My friends in the House tell me that if the bill passed the Senate by a decisive margin, they thought it could pass in the House."

The federal government has tried to transfer the two airports eight times since 1948. They are the only commercial airports owned by the government, which has undertaken few major improvements at either airport since Dulles was constructed in the early 1960s.

"This will come as a welcome relief to us," said Theresa Burt, an official with New York Air, one of the first airlines to concentrate its growth at Dulles. Like many airlines, New York Air has had to spend its own money on facilities at the airport.

The Reagan administration initially predicted an easy victory for the airport bill in the Senate. Trible and Warner said yesterday they believed that some of the changes, such as the decision not to sell the airports, would help the bill in the House, where the originally proposed $47 million sale price also had been criticized as too low.

Other amendments, such as one sponsored by Sen. Lloyd Bentsen (D-Tex.), are expected to generate additional opposition in the House. Bentsen's amendment would allow nonstop flights from National to go 1,250 miles, an increase from the current limit of 1,000 miles.

The amendment would allow direct service from National to Dallas-Fort Worth and Houston airports. The distance rule was designed to protect Dulles, which for years was underused.

Some House members from smaller cities are concerned that an increase in long-distance flights from National will result in fewer direct flights to their region. Rep. Gene Snyder (R-Ky.) the ranking minority member on the House Public Works and Transportation Committee, which will have jurisdiction over the bill in the House, opposes the wider perimeter rule.

"We have different opinions from our members on the effects of the perimeter rule," said Daniel Z. Henkin, spokesman for the Air Transport Association, which represents most major carriers and supports the bill. Some smaller airlines have said that the change in flight patterns would hurt them.

Another problem expected in the House is the issue of free congressional parking at the airports. Several House members have expressed concern that they might lose their privileges if there was a transfer because, under the bill, the authority could decide the matter.

Some House members also are worried about a provision in the bill allowing the commission to change the current nighttime noise restrictions at National, a move endorsed by both the airline industry and community activists.

Dole said that despite the hurdles in the House, she expects to see the bill enacted this year.

"We didn't come this far to sit back and watch it die in the House," she said. "It might be a battle, but I like a good fight."