Mayor Marion Barry created a task force yesterday to set priorities on which District schools will be repaired, following recent criticism by the D.C. Board of Education and City Council members about shoddy work and mismanagement on several school repair projects.

Barry also said in a letter to D.C. school board President R. David Hall that he is ready to explore "options in the contracting process," but did not elaborate.

Within one fiscal year, the task force is to set priorities for school building repairs, with roof repairs at the top of the list. It also is to monitor repairs on air conditioning systems, windows and doors, Barry said.

In December 1984, the school board protested to D.C. City Administrator Thomas Downs about various construction projects, such as a newly installed gymnasium roof at McKinley High School that was sliding off its moorings.

School officials have said the D.C. Department of Public Works had botched the handling of nearly 30 projects costing about $7.8 million, a fifth of the projects done from 1982 through 1984. School officials are seeking authority to award construction and repair contracts.

They particularly are concerned about roofing projects that were awarded to contractors who officials said did not perform on schedule, installed roofs that leaked, and in two cases went bankrupt before finishing the repairs.

Some City Council members said, after newspaper reports of the problems, that the city had been lax in awarding the contracts and in monitoring the projects.

Barry noted in his letter that he had proposed an increase in the school budget of $56 million for fiscal 1987, $20 million for operating costs and $36 million for capital improvements. This is not as much as the school board had sought.

Barry said his proposed funding "does not represent the total needs of the schools, but it indicates the high level of priority this administration places upon the education of our young people."

The task force is to consist of representatives of the mayor's office and the school board. Barry said he had selected Public Works Director John Touchstone, Public Works official Cyril Crandon and Julius Hobson Jr. of the office of intergovernmental relations.