WASHINGTON, Oct. 29 — State Department investigators offered Blackwater USA security guards immunity during an inquiry into last month’s deadly shooting of 17 Iraqis in Baghdad — a potentially serious investigative misstep that could complicate efforts to prosecute the company’s employees involved in the episode, government officials said Monday.

The State Department investigators from the agency’s investigative arm, the Bureau of Diplomatic Security, offered the immunity grants even though they did not have the authority to do so, the officials said. Prosecutors at the Justice Department, who do have such authority, had no advance knowledge of the arrangement, they added.

Most of the guards who took part in the Sept. 16 shooting were offered what officials described as limited-use immunity, which means that they were promised that they would not be prosecuted for anything they said in their interviews with the authorities as long as their statements were true. The immunity offers were first reported Monday by The Associated Press.

The officials who spoke of the immunity deals have been briefed on the matter, but agreed to talk about the arrangement only on the condition of anonymity because they had not been authorized to discuss a continuing criminal investigation.