Gasoline prices continue to fall in the Washington metropolitan area as oil companies and retail stations face heavy gasoline inventories.

Mobil Corp. lowered its wholesale gasoline prices yesterday by 2 cents a gallon on the East Coast, responding to recent price cuts by Exxon Corp. and several other major producers, according to industry officials.

Exxon cut 2.2 cents a gallon from wholesale gasoline prices Saturday in the Gulf and East Coast regions and smaller reductions were announced for California and Arizona. Shell Oil Co. cut wholesale gasoline prices by a penny in the Washington area late last week.

The latest reduction by Mobil left its wholesale price for regular leaded gasoline at $1.03 a gallon in the Washington area, down 5 cents since Oct. 3, a Mobil spokesman said. Similar reductions have dropped the price of regular unleaded to $1.07 a gallon and premium unleaded to $1.12.

The wholesale price cuts have generally been matched by reductions in retail prices at the pump. The national average retail price for all grades of gasoline fell to $1.346 a gallon in the first week of February, down 1.4 cents from December, according to a survey by the American Automobile Association. Retail prices have been declining since May, the AAA survey shows.

The current national average price is $1.345 per gallon, down 4.9 cents from the peak reached in April 1981, said the AAA, in its survey of 6,000 gasoline dealers nationwide.

The Energy Department's national average price of gasoline reached a high of $1.388 last March and has been dropping steadily since then, dropping to $1.348 in December. Two years ago, the department's average price was $1.186 a gallon, while in February, 1979, before the cutoff of Iranian oil had been felt, the price was 70.7 cents.

According to the AAA's February survey, the average price of leaded gasoline at full-service pumps in Washington, D.C. was $1.414 per gallon, compared with $1.347 in Maryland and $1.383 in Virginia. The average unleaded gasoline price at full-service pumps was $1.456 in the District, $1.397 in Maryland and $1.432 in Virginia.

At self-service pumps, the average leaded price was $1.253 in the District, $1.223 in Maryland and $1.255 in Virginia, while the average unleaded price was $1.349 in Washington, $1.304 in Maryland and $1.324 in Virginia.

The recent round of price cuts began in December, following a sudden growth in inventories of crude oil and petroleum products. Inventories had fallen during the summer and fall, but rebounded in December to the levels of the previous spring, as the recession slowed demand for gasoline and other products, said Townsend-Greenspan & Co., a financial consulting firm.

Oil companies are attempting to reduce inventories across a broad front. Gasoline shipments from refiners to wholesalers in January was down nearly 5 percent from January 1981, and major oil companies have reduced long-term contract purchases in the Middle East, industry analysts said. Purchases of crude oil on the world spot market have plummeted.