Alexandria School Superintendent Robert W. Peebles proposed yesterday that the city's school budget be increased by 8.59 percent to $60.2 million for the 1987 fiscal year.

The increase would be far higher than the 6.5 percent rise that City Manager Vola Lawson has recommended. But Peebles said that without the money the Alexandria schools could not hope to remain competitive with their neighbors in Fairfax and Arlington.

"We have a crisis before us," he said. "Alexandria could become a school system serving only poor and minority students." Peebles said that state funding formulas, which are based on tax revenues and demographics, do not provide fairly for Alexandria's large population of foreign-born and black students.

He said that the statistical mix of residents in the city does not accurately reflect who goes to school in Alexandria. Black residents, for example, make up only 22 percent of Alexandria's population, but account for 46 percent of the students in public school. More than a third of the city's 10,000 students come from low-income families.

He said that to keep Alexandria competitive with neighboring school systems, he would seek an average 7.7 percent pay increase for teachers. This would mean that the lowest salary for a starting teacher would rise from $18,200 to $20,000 in the coming fiscal year, about the same as has been proposed for Fairfax and Arlington.

For the first time, Peebles submitted three budget plans -- one that followed the city manager's guidelines, one that he suggested was the working plan calling for the 8.59 percent increase, and a budget that would provide for a 11.44 percent rise.

Peebles said that none of the three budget plans would call for a reduction in the teaching staff. His proposed budget plan would:

*Reduce all nonathletic field trips by 50 percent.

*Cut the level of special services in art, music and physical education.

*Totally restructure and consolidate the city's Academically Talented Program, for students in grades 4 through 6.

Peebles said that to maintain a commitment to improving minority achievement the schools would have to have more money to spend on fundamentals and would have to attract fine teachers. This year Alexandria students showed the widest disparity between blacks and whites in the region on standardized test scores.