The Senate last night approved measures that would force the Reagan administration to lift its controversial 76.4-mile limit on Metro subway construction and prohibit the U.S. Department of Transportation from lowering the ceiling on the number of passengers using National Airport.

The Metro provision, which has drawn widespread support from Washington-area members of Congress and other local officials, is aimed at overturning federal restrictions that have barred construction of major parts of the long-stalled Green Line and other sections of the proposed 101-mile rail system.

The National Airport measure, which has been opposed by members of Congress representing Northern Virginia, is designed to block a recent proposal by Secretary of Transportation Elizabeth Hanford Dole to reduce the cap on airport passengers to 15.2 million a year, 800,000 fewer than the current ceiling.

The Metro and National Airport provisions were included in an $11.7 billion measure to finance the nation's aviation, mass-transit and other transportation programs for the current fiscal year. The Senate, by voice vote, attached the transportation measure to a massive stopgap spending bill.

Aides to key House members said both the Metro and National Airport provisions appear assured of approval by House and Senate conferees after the Senate completes action on the spending bill. Despite earlier controversy over the issues, neither provision triggered any debate last night.

The Metro measure is considered likely to put pressure on the Reagan administration to approve the transit agency's recent plan for expanding the rail system to 89.5 miles by tapping funds previously authorized by Congress.

Dole praised Metro's plan earlier this week as a "highly positive step," but the administration has not announced whether it will approve it. Earlier this year, federal officials turned down a request by Metro for $24 million in federal grants, contending that funds were for construction projects outside the 76.4-mile limit.

Metro's plan for completing 89.5 miles includes two major rail extensions reaching beyond the 76.4-mile limit -- a Green Line branch between Fort Totten in Northeast Washington and Greenbelt in Prince George's County and a Yellow Line spur linking the King Street station in Alexandria with a proposed Van Dorn Street stop.

Metro officials have said they will eventually seek additional congressional authorization to finance the rest of the planned 101-mile system.

Advocates of lowering the cap at National Airport have argued that the move would reduce noise and other problems while encouraging greater use of Dulles and Baltimore-Washington International airports.

However, moves to restrict National's use have repeatedly set off opposition from the airline industry. Many members of Congress also have objected to limiting flights at the readily accessible airport.

The number of passengers using National has reached about 14.7 million a year, according to federal officials, and the total will climb slightly above 15.2 million a year by next summer if current trends continue.

Officials said it may prove difficult to reduce the cap to 15.2 million once the number of passengers using the airport exceeds that level. Dole previously had proposed a 14.8 million cap but retreated in the face of congressional opposition.