The Washington area's stepped-up efforts to help commuters arrange car pools have shown marked gains in recent years, according to a report released yesterday by the Metropolitan Washington Council of Governments.

The government-financed program helped find car pools for about 19 percent of the commuters who asked for assistance during the last fiscal year. Officials said this rate has risen steadily since 1981, when it was 12 percent. The rate was 13 percent in 1982 and 17 percent in 1983.

Jon M. Williams, the council's car-pool coordinator, attributed the gains largely to improvements in the computerized project, which seeks to match applicants with other commuters who want to form car pools. But he said the statistics also may signal a trend toward more car pools, especially to jobs in the downtown area.

The Washington area already has the highest car-pool rate of any major metropolitan area in the United States. According to the 1980 census, 355,886 commuters, or 22.9 percent of all workers, traveled to jobs in car pools of two persons or more.

Williams said car pools may increase partly because of a shortage of downtown parking spaces. "The number of parking spaces downtown is not going to increase," he said. "There's no place to put the cars."

The matching program, which is run by COG and several local governments, helped find car pools for about 4,700 out of more than 24,600 commuters who phoned (783-POOL) for help in the fiscal year ending last May. Officials said the area's car-pool projects cost about $400,000 a year.

According to COG estimates, the program reduced gasoline consumption by 786,000 gallons a year, saved commuters $2.1 million a year and helped curb air pollution by cutting yearly emissions of hydrocarbons by almost 12 tons.

Nearly 7,800 commuters who failed to arrange car pools through the matching program eventually joined pools through other contacts, officials said.

The program appeared most successful in arranging car pools for suburban commuters who travel long distances to jobs in central employment areas of the District and Arlington County. The program helped set up pools for 35 percent of the applicants from Prince William County, the highest rate in the area.

COG is seeking to expand its efforts by opening two car-pool offices at major federal employment centers: one at the Pentagon and another at the Department of Health and Human Services in Southwest Washington. The Virginia Department of Highways and Transportation has recently earmarked $15,000 to post signs on highways to encourage car pools.