The Fairfax City Council has cut 6 cents from the city's real estate tax rate, but officials acknowledged yesterday that rising real estate assessments will continue to boost the tax bills of local residents.

"Even with the decrease in the tax rate, it looks like the average person will be paying more," said council spokesman Thomas B. Welle.

Under a $22.2 million annual budget adopted by the council Tuesday night, the city's tax rate will drop from the current $1.30 per $100 of assessed value to $1.24 in the next fiscal year. That means a family living in a home in Fairfax City that has an assessed valuation of $83,000 will pay approximately $1,030 in taxes next year.

The same family would have paid approximately $960 in real estate taxes during the last fiscal year, when their home would have been assessed at about $73,000.

City Manager George E. Hubler Jr. had proposed a tax rate reduction of only 1 cent, but Welle said the council was able to cut the rate further based on estimates that the 1-cent local sales tax will bring in approximately $631,000 more during the next two years than had earlier been predicted.

Hubler had also recommended a 9.1 percent salary increase for the city's 260 employes, but the council reduced that increase to 8 percent.