"This department met yesterday with all of our senior staff and we have instructed that if we learn of anyone who has traveled to this event, the president's remarks, or was present in Washington, D.C. on Jan. 6, that we're to identify them and identify their involvement,'' Moore said.
The department will determine if identified officers engaged in illegal activity, but regardless of conduct, anyone who attended will be ordered to provide an interview with the FBI, Moore said, as officers may be able to provide information about others who engaged in criminal activity at the Capitol.
When asked Tuesday if he was aware if any officer was in D.C. on Jan. 6, Moore said he knew of one employee who attended President Donald Trump's speech, but didn't participate in the violence that followed.
"Currently I'm aware of one employee that traveled and participated by attending the speech of President Trump and his report was he left prior to any other activity and did not participate in anything that occurred at the Capitol, and that he was back at his accommodation and observed it as many other shocked Americans did on television," Moore said to reporters.
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The person will be interviewed by the FBI in its inquiry, Moore said.
"If I learn of any misconduct or criminal act by anyone in the organization, they'll face a swift response in our actions," Moore said.
He said he has ordered his officers to come forward if they were in D.C. on Jan. 6 and explain what their activities there were.
"Anyone that we identify that has traveled will be ordered and directed to provide an interview with the FBI, as they are interested in witnesses, and in identifying people who did commit criminal conduct, but also witnesses that were there that may add information as they pursue those criminal acts that were completed that day," Moore said.
Moore added there is strong difference between those who committed crimes at the Capitol and those who gathered to listen to the president's speech and didn't participate in the riot.
While Inauguration Day gets closer, Moore says they're monitoring any information or tips that come in locally and across the country to make sure L.A. stays safe.
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"There is no specific and/or credible information about any attack or threat of violence against any building, public facility, government structure in the Los Angeles area of operation," Moore said when asked if L.A. has been mentioned as a possible location of violence ahead of the inauguration or if any places were more at risk of being targeted.
He says there will be an increased police presence starting the end of this week and into next week.
"We'll have added staffing in substantial numbers around our downtown business core, around our Civic Center as well as other critical spots in the L.A. region as we approach the inauguration and on the day itself and into the evenings each night," Moore said.
Also on Tuesday, four L.A. City councilmembers introduced a resolution supporting the second impeachment of Trump for alleged incitement of an insurrection.
Councilman Paul Koretz referred to Trump's behavior as that of a madman and said he presents a danger to the U.S.
Trump has denied any culpability in the violence.
City News Service contributed to this report.