The Alexandria School Board approved a $41 million budget request last night that is 16 percent higher than the current budget largely because of higher fuel costs and plans to raise teachers' salaries.

The budget, which outgoing school Superintendent John L. Bristol said "attempts to address reality," now goes to the City Council for funding and final approval.

Bristol noted a request by City Manager Douglas Harman that the school system limit its budget request to 8 percent over current spending. He said the need to pay teachers a competitive wage so they will remain with the city's schools was the principal factor in the proposed budget increase, twice the limit Harman proposed.

The 12.5 percent raises Bristol reccommended for the city's 801 public school teachers are designed to help them "catch up" with teachers in surrounding jurisdictions. Alexandria teachers now are paid an average of $19,000 a year, several thousand dollars less than teachers elsewhere in Northern Virginia, officials said.

Bristol also told the board that the increased cost of fuel to heat buildings and run school buses added nearly a half million dollars to the budget request.

The teachers' 12.5 percent raises would be in addition to a 2 percent raise the school board voted last night to give all school employes. It parallels a 2 percent increase granted municipal workers by the council last week and goes into effect in April.

The council provides almost all of the school system's budget, and in the past the two powerful bodies have argued heatedly over how much money the school board should get, and how it should be spent. The school budget represents more than one-third of the city's expenditures which this year are more than $94 million.

Last week the council imposed budget limitations on itself, voting to limit the 1980-81 budget to no more than $107 million. That limitation may have an impact on how much money is allocated to the schools.

The board appeared to take the council's budget limitation into account, voting to seek a closed-door session with the council to explain its budget request.

The budget was approved on a 6-to-2 vote. Board member Michael Mulroney voted against the budget, saying the increases were too small to maintain a quality school system. Member Harvey Harrison voted against it, saying the proposed budget was "too much for taxpayers to pay."