The Brooklyn district attorney said on Friday that he planned to impanel a grand jury to look into the death of Akai Gurley, an unarmed Brooklyn man who was killed last month by a police officer patrolling a public-housing unit.

With protests continuing over the grand jury decisions not to charge the officers who killed Eric Garner on Staten Island and Michael Brown in Ferguson, Mo., the tension around the Gurley case has also risen. Mr. Gurley was black, as were Mr. Garner and Mr. Brown. The officers in the Garner and Brown cases are white; the officer who shot Mr. Gurley, Peter Liang, is Asian-American.

The district attorney, Kenneth P. Thompson, said in a statement that he did not support the appointment of an independent prosecutor to handle the case, saying he had been elected by Brooklyn’s residents to represent their interests. “It is important to get to the bottom of what happened,” he said.

Mr. Thompson added, at an event on Friday, that prosecutors had not completed their investigation, so the timing for the grand jury was not yet clear.