The Senate approved an amendment yesterday designed to block a controversial move by the Department of Transportation to permit airlines to buy and sell valuable landing rights at National and three other major airports.

The approval, on a vote of 82 to 12, came as the Senate began considering several amendments to a bill to transfer National and Dulles International airports from the federal government to a regional airport authority. The measure is strongly supported by Virginia elected officials and the business community, but is opposed by Maryland officials.

Virginia senators succeeded in fighting off attempts to alter the measure, and Sen. Paul S. Trible (R-Va.), floor manager of the bill, predicted that the Senate would complete work on it by tonight or tomorrow.

The amendment on so-called landing rights, which was proposed by Sen. Nancy Kassebaum (R-Kan.) and is opposed by the Reagan administration, does not affect the airport transfer plan.

Under a Transportation Department rule that went into effect April 1, airlines were permitted to sell landing rights at National, O'Hare at Chicago and La Guardia and Kennedy at New York, four of the nation's busiest airports. The rule could mean a windfall for some airlines that hold the rights, for which they paid nothing.

The amendment would create a scheduling committee, appointed by the federal aviation administrator, to allocate underused landing rights or slots. If the scheduling committee is unable to decide how to allocate the slots, other methods, including an auction or lottery, could be used. All funds generated would go back to the federal government for airport improvements.

The bill to transfer National and Dulles airports to a regional authority -- a Reagan administration proposal -- was filibustered for more than a week before the Easter recess by Sen. Paul Sarbanes (D-Md.) in an effort to kill it. Supporters expressed dismay over his success in delaying action.

Several sources said that prospects for passage of the bill improved yesterday as a number of Republicans lined up behind the proposal. Most Republicans and about half the Democrats were counted in the Virginia camp last night, according to some supporters and opponents of the bill.

Sarbanes said Secretary of Transportation Elizabeth Hanford Dole "has been lobbying everyone hard. We'll see what happens." But he added that he still thought that the votes on amendments have been close enough to indicate that a number of senators have problems with the way the plan for the airports is drawn up.

One amendment defeated yesterday would have changed the composition of the airport authority board, which, as proposed in the bill, would be heavily weighted in favor of Virginia. Sen Larry Pressler (R-S.D.) proposed, among other things, giving Virginia two representatives on the commission, instead of five. That amendment lost by eight votes, but another Pressler proposal, to increase the number of presidential appointees on the board from one to three, was accepted.

The Senate also defeated a sense-of-the-Senate resolution by Sen. Frank Lautenberg (D-N.J.) urging the Reagan administration to rehire fired air controllers.

Sen. Gordon Humphrey (R-N.H.) withdrew an amendment that would have opened bidding for the airports to private investors. He argued that the federal government could get more money from such investors, but Virginia officials said the amendment would provide major obstacles to the airport sale.