(CNN) 2020 Democratic presidential candidate Kamala Harris now says she believes that cases of fatal police shootings and alleged police brutality should be handled by an independent investigator -- a change in her stance on the issue.

"I believe the best approach is to have independent investigations. There is no question," Harris, a former career prosecutor, said in an interview on MSNBC Monday.

Harris previously held the view that local elected officials should continue investigating potential criminal cases against police officers.

"I don't think it would be good public policy to take the discretion from elected district attorneys," Harris, then California's attorney general, told the San Francisco Chronicle in 2014. "I don't think there's an inherent conflict. ... Where there are abuses, we have designed the system to address them."

Harris told MSNBC on Monday that it was a "personal experience" during her time as district attorney of San Francisco that had informed her prior thinking that cases shouldn't be taken from locally elected prosecutors.

As the city's top prosecutor, Harris had refused to seek the death penalty in 2004 for the killer of San Francisco police officer Isaac Espinoza.

"There were people who didn't agree with my decision and wanted to take the case from me," Harris recalled. "And so, I had a very real, personal experience where I had to fight to keep my case — and my argument was that, 'I was elected to exercise my discretion, and no one's going to take my case from me.'"

But Harris said incidents of police shootings and alleged police brutality are a "different issue."

"There's got to be an independent investigation conducted from the first moments of the incident, so that we can be certain and sure that there has been a thorough investigation that is not informed by bias and so that there will be justice for all of the people concerned," Harris said.

During a CNN town hall in January , Harris was asked by moderator Jake Tapper why, as California attorney general, she had opposed legislation in 2015 that would have required her office to investigate fatal shootings involving police officers.

Harris said she did not weigh in on the bill at the time, or any other legislation or initiatives, because she felt it was a conflict of interest with her job as the state's top law enforcement official.

The Washington Post also found that Harris had taken a stance on a range of pending bills and at least one proposed ballot initiative. Harris' spokeswoman told the Post the senator had misheard Tapper's question and misspoke in response.

Since announcing her presidential bid, Harris faced increased scrutiny over her criminal justice record and criticism pushing back on her assertion that she was a "progressive prosecutor," reforming the criminal justice system from within.

Harris's campaign has pushed back on that criticism, pointing to her initiative as attorney general to start the first statewide implicit bias and procedural justice training, require body cameras for Justice Department agents, and push for data on in-custody deaths and police shootings to be made publicly available.