"He is not a king. He cannot 'defund' NYC," New York Gov. Andrew Cuomo said. "It's an illegal stunt."
Democratic challenger Joe Biden on Monday said it was Trump himself who was helping stoke the violence.
Authorities have not identified the shooting victim. But the New York Times reported the man gunned down was wearing a hat with the insignia of the right-wing group Patriot Prayer.
Protests have roiled downtown Portland every night for nearly three months following Floyd's death, and police there said they had made arrests after one person was shot to death on Saturday night.
Caesar, the six-year-old "No Drama Llama," has become a fixture in the city, extending his wooly neck to nuzzle both Black Lives Matter activists and law enforcement officers in body armor.
The ongoing protests in Portland have been escalating due to backlash against the use of federal agents, which Trump has suggested sending to multiple cities across the US.
Rosenblum, who was elected to her post in 2012, is a former board member of her Portland synagogue.
Tuesday will mark the first time that Barr has appeared before the House Judiciary Committee since taking the helm of the Justice Department in February of last year.
The tactics, condemned by Democrats as federal overreach, have fueled a new wave of protests following demonstrations sparked by the death of George Floyd in police custody in Minneapolis on May 25.