The White House did not immediately respond to a request for comment.
Flags at the Capitol building were lowered to half-staff on Friday, under an order from House Speaker Nancy Pelosi, California Democrat.
Officer Sicknick, 42, was bludgeoned to death with a fire extinguisher and died of his injuries late Thursday at a Washington hospital. His death is under investigation as a homicide.
Mr. Trump ran one of the most-pro law enforcement campaigns in recent history, with police unions enthusiastically endorsing him for president.
Multiple law enforcement groups that endorsed Mr. Trump have turned on the president since his supporters mobbed the Capitol, resulting in injuries to more than 50 law enforcement officers.
“It’s bad enough that there have been attacks on law enforcement from the left and now they have it from the right,” he continued. “Our nation’s leader incited the violence and someone needs to be held accountable, and it’s him.”
Mr. Trump ran one of the most pro-law enforcement political campaigns in recent memory and the police responded. Police unions across the country mobilized like never before to support Mr. Trump ahead of the presidential election. Even union chapters that have never endorsed political candidates sided with the president because of his support for law enforcement.
But after a Capitol Police officer was killed during the violent riot at the Capitol, they feel betrayed by the president. Adding insult to injury is that after Officer Brian Sicknick died from injuries sustained during the insurrection, Mr. Trump still hasn’t contacted his family and that the White House flag wasn’t lowered to half-staff in his honor until Sunday afternoon.