Fairfax County and Alexandria said yesterday that their residential property values increased last year at their slowest rate in almost a decade, confirming that the region's once booming suburban housing market has cooled dramatically.

Residential assessments in Alexandria grew at a rate of 1 percent, so slowly that some city officials were warning that higher real estate taxes seem a certainty. Not since 1974, when the city began making annual reassessments, has the increase been so small, the officials said.

In Fairfax County, where officials already had predicted a modest increase in residential assessments, the typical value of a house increased by 1.4 percent, the smallest increase in more than a decade. The increases in both Fairfax and Alexandria were in line with those reported in the District and Arlington where home values fell last year by 2 to 3 percent.

In Alexandria, city officials said only houses located near the city's completed but unopened Metro stations and a relatively small number of houses valued at more than $200,000 showed increased value.

"What it may mean," said Vice Mayor James P. Moran Jr., "is that it's going to be really tough not to raise property taxes more than 5 cents, which is our upward cutoff. It's going to make it harder to stay with that."

Mayor Charles E. Beatley and others on the City Council have said that they favor seeking alternative sources of revenues this year rather than turn to massive increases in the property tax rate, which is currently set at $1.37 per $100 of assessed value.

The low increase in residential property values surprised some Alexandria officials and Moran said it may force the council to consider drastic cuts in spending. "It's going to mean we are going to have to cut out some programs, reduce services, and perhaps, make reductions in personnel," he said.

Bradford Hammer, Alexandria's deputy city manager for finance, also said the low rate of increase will force "some changes. The city cannot afford to balance the budget on the type of static property appreciation that is the result of the 1983 assessment."

Hammer said it is too early to discuss what course the city may choose. A final report on the impact of the new assessments is scheduled for early next month.

Real Estate Assessment Director David Chitlik said of the city's 25,000 residential properties, about 650 parcels in the Rosemont neighborhood and town houses in the Del Ray section had higher assessments. Both areas are near the King Street and Braddock Road Metro stations and saw their assessments increase by about 5 percent.

The first batch of Fairfax County's property assessments -- about 50,000 notices -- will be mailed Thursday, county officials said yesterday. All property owners whose assessment has changed should receive a notice by the end of the month.

Overall, property assessments in Fairfax are expected to rise an average of 2.5 percent, but most of that will be borne by commercial properties, officials said. Assessments for commercial and industrial property and for apartment houses will increase an average of 7 percent, although the values will vary widely, according to county officials.

The values of residential properties, which comprise the bulk of the county's tax base, will rise an average of 1.4 percent, but they also will vary greatly, according to the county. Assessments for single-family detached homes, in most cases, will stay the same or fall slightly. Those for town houses and condominiums probably will increase more than the average 1.4 percent.

Assuming the county supervisors accept the budget for fiscal 1984 proposed by County Executive J. Hamilton Lambert, Fairfax's property tax rate will remain at $1.47 per $100 assessed valuation.

E.M. Stever, president of the Fairfax County Taxpayers Alliance, noted that the assessment increases were far less than in recent years. But he added: "To be perfectly cynical, this is an election year. Just wait until next year. Oh boy, we'll get right back on that steep, increasing curve again."