The average assessed value of single-family houses in Arlington will drop 2.8 percent this year, reflecting the depressed Washington real estate market and prompting county officials to take the first step toward a possible increase in real estate taxes.

The drop in assessments, believed to be the first decrease in the county since the Depression, was disclosed yesterday as the county board began deliberations for its 1983-1984 budget. Until yesterday, county officials had been predicting that property assessments would be unchanged or slightly increased this year.

After being told of the decline and possible increases in county spending, the board's Democratic majority voted to advertise a possible increase in the real estate tax rate from 98 cents per $100 assessed valuation to as high as $1.01.

"I'm doing this out of what I hope is an overabundance of caution at this point," said Democratic board member John G. Milliken. "I don't see any reason to cut off our options before we know what the situation will be with the school board and Metro and with the federal and state governments."

The board's two independent-backed Republicans, Dorothy T. Grotos and Walter L. Frankland Jr., who are up for reelection this fall, opposed advertising a higher tax rate. Frankland said the Democrats' actions were a political ploy.

"It's my conviction that the majority has no intention whatsoever of adopting that rate and when the time comes, they'll adopt a lower rate, most likely the 98 cents," he said. "This will make them look as though they were being very careful in their approach to this and in the end will come forward as being concerned about the tax rate and they'll vote the lower rate."

County Manager Larry J. Brown, who told the board the assessments had dropped and who recommended the higher advertised rate, said his proposed $224 million fiscal 1984 budget could be balanced at the current rate.

Brown also told the board that the county had $600,000 more to spend in fiscal 1984 than previously estimated, because of decreased costs and increased revenues.

The board, which will set the real estate tax rate March 19, cannot increase it beyond the advertised rate. The board has scheduled a hearing on the tax rate and proposed fiscal 1984 budget for 7 p.m. March 15 at Kenmore Intermediate School.

The average Arlington house in 1982 was assessed at $114,123 and the owner paid $1,118 in real estate taxes, Brown said. This year, that assessment will drop to $110,945. If the tax rate remains the same, the owner would pay $1,087--half in May and the remainder in October. If the rate goes up to $1.01, the owner would pay $2 more than last year, or $1,120.

If the rate remains the same, the county would collect $700,000 less in real estate taxes from homeowners than last year. Assessments have risen for commercial property and apartment buildings, so overall the county's assessments will increase 0.4 percent, Brown said. The $2.3 million in revenues from those properties will offset the $700,000 reduction in homeowner taxes, for a net increase of $1.7 million in property taxes on real estate.

Anton S. Gardner, chief of the county's financial management section, said assessments on single-family houses have declined this year because of the slumping real estate market.