A bleak weekend for gasoline sales began yesterday in the Washington area as most stations stayed closed to conserve their dwindling June allocations and mile-long lines greeted motorists who needed gas.

Maryland state police said that mile-long lines clogged traffic yesterday morning near the few stations that were open; Virginia state police said that lines of 200 cars were reported to open stations in Arlington. There were similar lines in the city.

The local American Automobile Association predicted that only 5 percent of area stations would be open today. Eight designated stations will be open from 8 a.m. to 1 p.m. in the District of Columbia, using special allocations of gas from the city's "setaside" reserve program.

Yesterday's crunch at open stations came after two days in which lines shortened somewhat under the government-imposed odd-even sales plan in the District, Maryland and Virginia. Under the plan, Saturday and Sunday are "open" days when all drivers may buy gas.

The problems seemed to be worse in the outlying areas of Maryland and Virginia. Motorists in St. Mary's County in southern Maryland lined up as early as 4 a.m. to buy gas, state police said, and there were reports of lines as long as 2 1/2 miles. Long lines were also reported in Calvert and Charles counties, police said.

Meanwhile, about 40 residents of the Dale City, Va., area about 30 miles south of Washington assembled yesterday in Dale City to hear a panel discussion by local and federal energy officials and plan a march on Washington next month by frustrated commuters.

Virginia Rep. Herbert E. Harris II appeared at the meeting and released a study that he said showed that oil company storage tanks in Fairfax City had been filled with 13 percent more gas this year than in 1978.

Harris called last week for an investigation of the gas tanks after reports that bulk storage tanks of several major oil companies in Fairfax contain more gasoline than normal, even as motorists are forced to wait in service station lines.

Harris' study showed, for example, that storage tanks in Fairfax City for Gulf, Amoco and Texaco received 2.2 million barrels of gasoline in May, compared to 1.9 million in May, 1978.

Dale City commuters at the meeting were clearly angered. "I actually missed two days of work last week because I couldn't get gas," said one, Doris Lancaster. "I had to tell an attendant I would go out on two dates with him before he would give me gas."

Part of the problem yesterday in the local area, dealers said, was end-of-the-month shortages at stations with gas allocations generally reduced by more than 15 percent below last year.

The situation was summed up by Alejandro Creque, whose Homoco station at 11th Street and Rhode Island Avenue NW opened yesterday but did not sell gas because, Creque said, "We've been dry since the 15th of the month."

Creque said he could not sell gas again until July 1, when he will receive a new shipment from his supplier, the Homes Oil Co.

The stations open today in the District from 8 a.m. to 1 p.m. with special gas allocations are: Lindsay Patrick Amoco, 814 Bladensburg Rd. NE; Carl's Sunoco, 2510 Pennsylvania Ave. SE; Lloyd's Exxon, 415 Rhode Island Ave. NE; Steven's Exxon, 5831 Georgia Ave. NW; "L" Street Exxon, 1100 13th St. NW; Colonial Exxon, 3227 M St. NW; Parker Gulf, 1200 South Capitol St. SE, and Morin and Captain Amoco, 4300 Connecticut Ave. NW.