President Reagan's proposed budget for fiscal 1984 would make drastic cuts in construction funds for the Washington region's subway system and would delay by a year or more the scheduled openings of subway extensions and two new lines, Metro officials said yesterday.

The transit agency got $285 million for its fiscal 1983 federal allocation and had asked for $375 million for its 1984 construction program. The Reagan budget sent to Congress yesterday would allocate only $230 million for subway construction here during 1984.

"We expected we'd get something in the neighborhood of $300 million, but this looks pretty devastating," said William A. Boleyn, assistant general manager and comptroller for Metro.

Predicting that the Metro board would seek funding restorations in Congress, Boleyn said the president's proposed budget would provide the smallest amount Metro has received in federal funds since 1975. He warned that failure to boost the allocation would force Metro to juggle its construction schedule and its method of assessing jurisdictions for building costs.

That would foul up Metro's timetable, Boleyn said, noting that construction and station openings would be delayed on the Orange Line leading to Vienna from mid 1986 until mid 1987, and on the Red Line leading to Glenmont from late 1988 until late 1989.

He added that it also would push back the openings of the new Yellow Line to Springfield-Franconia from 1990 to 1991, and the new inner city Green Line route between Shaw and Anacostia from late 1989 until the early 1990s.

Administration officials, according to Boleyn, have suggested that Metro augment its construction funds with new money it expects to receive from the recently enacted five-cent gasoline tax increase.

But Boleyn said the gas tax money was envisioned as paying for Metro's other transit needs. At most, he said, Metro had expected the gas tax to produce $74 million--all of it targeted for badly needed bus rehabilitation, rail repairs, reductions in the operating subsidy and, possibly, the purchase of new buses.

While the president's budget was a shock for Metro, it appeared to have some good news for National Park Service spending in the District, Maryland and Virginia.

The proposed budget would enable the Park Service to make needed improvements in the drinking water, sewage and utility systems of various Washington area parks and tourist spots, according to spokesman Duncan Morrow.

The heating and ventilation system at the White House, last renovated during the Truman administration, would be overhauled at a cost of about $3 million, he said. Comfort stations in the Mall and Potomac Park would be replaced for about $1 million. An additional $624,000 would be spent to install two sewage stations in East Potomac Park.

In Maryland, $3 million would be spent to replace drinking water systems at Catoctin Mountain Park near Camp David.

In Virginia, $1.3 million would go to rehabilitate or replace deteriorating buildings at the group camping area in Prince William Forest Park adjoining the Quantico Marine Base. Fredericksburg National Military Park officials would spend $190,000 in federal funds to improve the fire protection and water system at the Stonewall Jackson Shrine there.