The Fairfax County Board Supervisors ruled out an increase in the real estate tax rate yesterday but left itself the possibility of lowering the rate before May 8 when it adopts the budget for the 1978-79 fiscal year.

The supervisors are considering using some of an $8.4 million budget surplus this year to lower the current rate of $1.74 per $100 of assessed valuation.

The board's decision yesterday authorizing an advertisement of the current rate for the fiscal year that begins July 1 eliminates the possibility of a tax rate increase.

Even if a tax rate cut is agreed on, the homeowner's tax bill will not necessarily decrease. That is because the value of county real estate is still climbing. Countrywide, assessments rose an average of 8.7 percent in 1977, compared to 7.2 percent on 1976. That means that the owner of a $60,000 house who paid $1,044 in real estate tax last year would pay $1,134 this year if there is no change in the rate.

Six of the nine supervisors have said they would favor decreasing the tax rate this year. Two others said a cut is possible and one declined to comment. Most of the supervisors supporting a rate cut said they thought a reasonable decrease would be between 3 and 5 cents.