ALBUQUERQUE — After demonstrations over a string of fatal shootings by the police became so heated over the weekend that officers in riot gear lobbed tear gas at an unruly crowd, the governor of New Mexico and Albuquerque city officials urged calm on Monday and reassured a jittery public that investigations of the shootings were underway.

“Albuquerque is going through a tough time, and they’ll figure it out through the investigation,” Gov. Susana Martinez said at a news conference, referring to the killing last month of James Boyd, 38, a homeless man. “We want that to be thorough,” she said. “We want confidence in the investigation, but I just don’t want to see anyone harmed.”

Hundreds have taken to the streets in protest here in recent days over the shootings of Mr. Boyd and other people who most likely had mental illnesses, episodes that have weakened the public’s confidence in the Albuquerque Police Department and underlined the challenges faced by police officers when dealing with people with mental illness. In all, 23 civilians have been fatally shot by the police, and 14 others have been wounded since 2010, a series of events that has prompted a broader federal investigation into the department’s use of force.

The victims have been of various backgrounds. The first, Kenneth Ellis III, 25, was an Iraq war veteran struggling with post-traumatic stress disorder, shot while holding a gun to his head in January 2010 at a gas station parking lot, where he had been pulled over by the police over suspicions of driving a stolen vehicle. One of the most recent, Mr. Boyd, was killed after pulling out a pair of knives during a lengthy argument with the police over his illegal camping on a mountainside.