The Falls Church City Council approved a $17.5 million budget last night for the fiscal year that starts July 1 that calls for no increase in the city's real estate tax rate.

But taxes for most homeowners will still rise. A 5.2 percent increase in assessments in the last year will raise taxes for the owner of the "average" $126,700 single-family detached house by about $62, to $1,242. Last year, that same house was assessed at $120,400 and the owner paid a tax of $1,180, city Assessor William De Lanoy said.

Mayor Carol DeLong said the council was able to cut $150,000 from the budget proposed by City Manager Anthony Griffin and to avoid the 2 cent increase in the tax rate he suggested because of factors that include a $104,000 reduction in the city's contribution to Metro and a $62,000 reduction in the School Board's request for city funds.

The tax rate remains 98 cents for each $100 of assessed valuation.

The budget, which represents a $1.5 million, or 9 percent, increase over current spending, includes a 4 percent cost-of-living raise for the city's 250 employes, according to Barbara Gordon, spokeswoman for the city government.

The raise approximates the increase in the federal consumer price index for the last year, she said.

The council earmarked $5.7 million for schools, the full amount requested by the School Board to help fund the board's operating budget, which totals $7.4 million. Overall school spending will increase about 12 percent during the next fiscal year.

The School Board's budget calls for about $500,000 to pay higher salaries.

It endorses a pay schedule that would increase pay for new teachers to $18,040.

This school year, Falls Church teacher starting pay of $15,700 is the lowest in Northern Virginia. Starting salaries in the counties of Arlington and Fairfax and in Alexandria were $18,670, $18,385 and $18,200, respectively.

Next fall, starting salaries in Arlington and Fairfax counties will be $20,100 and $20,000, respectively. The Alexandria City Council has not yet adopted its budget.

According to Wayne Moore, Falls Church public schools business manager, the School Board's budget will raise the average teacher salary from $29,296 to $31,675.

The city's $3.6 million capital improvement program for fiscal 1987 will include $1.8 million for 14 water utility projects, $552,000 to help pay for reconstruction of Broad Street from Haycock Road to West Street and $135,000 for architectural fees for the future renovation of the Mount Daniel Elementary School.