Most Washington-area subway construction would stop in fiscal 1983 under President Reagan's budget proposals, but there will be strong lobbying on Capitol Hill to increase outlays for Metrorail, General Manager Richard Page said. The Metro system has faced funding threats repeatedly since ground was broken for the project in 1969.

Reagan's budget would gut most of the 1983 money scheduled for tunneling on the inner-city Green Line; finishing work on the Orange Line extension to Vienna; construction of the Red Line extension to Glenmont, and other construction or real estate purchases planned for lines to Greenbelt, Rosecroft and Franconia/Springfield.

It would not affect construction of the Red Line extension to Shady Grove, scheduled to open in late 1983, the Yellow Line from Gallery Place to National Airport and the Blue Line extension to Huntington, according to Metro officials. The Yellow and Blue Line segments are scheduled to begin operating late this year, although delayed delivery of rail cars probably will push those openings back.

The 1983 budget and earlier federal cutbacks have raised fears among area governments that much of Metro's planned 101-mile rail system, 39 miles of which now are in operation, never will be built. In the budget document released Saturday, the administration reaffirmed that it is committing itself only to building a 75-mile system for the time being.

Almost every year a grave threat to Metrorail has loomed on Capitol Hill, officials point out, but each time a compromise has been achieved to keep the work crews on the job, if not on schedule. Metro officials have until the fall to lobby Congress against Reagan's proposal and say they could turn back this threat, too.

"We did pretty well last year on the Hill," Page said. Federal funding for the rail system grew from $275 million in fiscal 1981 to $284 million in this fiscal year, despite administration efforts to trim the federal budget.

But the proposed 1983 budget confirmed the bad news that Metro officials have been hearing privately for months. The White House wants to limit rail construction funding to $295 million: $100 million from funds approved two years ago under legislation known as the Stark-Harris bill and $195 million from "interstate transfers"--trade-ins on unbuilt interstate highways.

But Metro could in fact get only about half that sum. The D.C. government, which holds veto power over the transfers' use because the highways were to be built in the city, intends to keep most of the transfers for itself.

As administration officials have been told repeatedly, the city long has planned to reserve about $150 million of the transfers for a five-year program to repair its badly weathered roads and bridges. That would leave about $45 million in transfers for Metro. Combined with Stark-Harris funds, the subway would get only $145 million in capital funds.

That would mean a virtual halt in construction, Page said. "It is simply enough money to close out the current contracts and make payments for additional rail cars and cover contingency and insurance and other expenses." The four-year building program Metro now is implementing is counting on federal aid of $375 million for fiscal 1983. Federal funds now cover about 85 percent of Metrorail's building costs.

D.C. already has given more than $2 billion in interstate transfers to Metro, according to Transportation Department head Tom Downs, and intends to reserve the $150 million for its neglected roads. Page said that because the streets are in bad repair, Metro will direct its lobbying at Congress, to try to raise funding from the Stark-Harris bill.

That bill, signed two years ago by then-President Carter, approved $1.7 billion in capital funds for Metrorail, to be paid out in parcels as approved by Congress.

But the administration is fighting to curb the overall federal deficit in fiscal 1983 and wants to hold Stark-Harris funding to $100 million that year, though the rest of the $1.7 billion still would be available in later years.

Page said that if lobbying efforts fail, D.C. would be faced with a difficult decision: to delay the road repairs further or let subway construction halt. That would stop work on the largely unbuilt inner-city Green Line linking Anacostia and U Street NW. Mayor Marion Barry has placed a high priority on keeping construction going there.