Alexandria Police Chief Charles T. Strobel, saying he faced many unfinished tasks, announced yesterday that he has withdrawn his application to become executive director of the Florida State Department of Law Enforcement.

Strobel, 42, who has presided over the Northern Virginia police force during a period of sharp controversy, said he wanted to complete certain unspecified programs within the 238-member department.

A lifelong resident of Alexandria and a member of the force for 21 years, Strobel said recently he filed his application for the Florida position after being approached at a police convention. Strobel has said in the past that he would consider leaving Alexandria only it the "right position came along."

The department has been both praised and criticized for its handling of bingo games, murders, massage parlors, and prostitution investigations under Strobel's two-year tenure as chief.

One of the department's most vocal critics, City Councilman Donald C. Casey, indirectly expressed praise for Strobel at recent council budget hearing, saying that Strobel possibly might be given a salary raise in order to keep him from moving to Florida. Strobel currently earns $35,289.

No action has been taken on Casey's suggestion by the council.