In a statement read by the council's chairman, Phil Mendelson, Mayor Muriel Bowser said she was supportive of the legislation but thought there should be a public discussion.
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D.C. police chief Peter Newsham told a news conference Monday the department had already made a number of reforms in the past two decades and would discuss concerns it had with Charles Allen, the council member who introduced the legislation.
Most Americans support the protests, which have been largely peaceful, and disapprove of U.S. President Donald Trump's reaction to them.
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In 2001, the U.S. Justice Department found Washington, D.C.'s Metropolitan Police Department had a pattern or practice of excessive force as well as other issues. The investigation led to federal oversight of the department, including the appointment of an independent monitor, until 2012.