President Trump could make a major address to the nation regarding policing and the recent protests over the death of George Floyd in Minnesota, White House aides say, according to a new report by CNN.

Aides to the president have reportedly been discussing plans for a speech in recent days in response to widespread bipartisan backlash to the president's response so far, which has included a tweet that read "when the looting starts, the shooting starts," a phrase that earned criticism from many, including some GOP members of the Senate.

Housing and Urban Development Secretary Ben Carson hinted as much during an interview with CNN's "State of the Union" on Sunday.

"I believe you're going to be hearing from the president this week on this topic in some detail. And I would ask you maybe to reserve judgment until after that time," he said.

At the same time, CNN reported that some Trump advisers think the president can double down on his "law and order" message, even though he came under criticism last week because of it.

These advisers argue that the reduction in violence since Trump's statement last Monday would allow him to argue his actions have been effective.

The White House did not immediately return a request for comment from The Hill on CNN's reporting.

Trump's handling of the protests has created some frictions within the GOP.

Sen. Mitt Romney (R-Utah) joined protests in Washington on Sunday, and some GOP lawmakers have joined in on the criticism of the president. 

"I have not spoken with the president in the last few days. I do think some of his tweets have not been helpful, and it would be helpful if he would change the tone of his message," said Sen Pat Toomey (R-Pa.), according to USA Today.

Floyd was killed on Memorial Day when a white Minneapolis police officer detained him and then pinned him to the ground with his knee on Floyd's neck for nearly nine minutes. Outrage over Floyd's death has led to nationwide protests and calls to defund police departments and to enact other reforms.