Brian D. Sicknick responded to the rioting Wednesday and "was injured while physically engaging with protesters".
The family asked the public to respect its wishes "in not making Brian's passing a political issue".
"Brian is a hero and that is what we would like people to remember", a statement from the family reads.
"(They) weren't protesters. Don't dare call them protesters.
"These People are not protesters or patriots, they are domestic terrorists who were beckoned by the dog whistle of Donald Trump", Barbuto wrote. "They will not be disrespected or treated unfairly in any way, shape or form!"
Joe Biden will become president January 20.
Her last Twitter post was on Wednesday, before Trump urged his supporters to march to the Capitol, where lawmakers were debating the Electoral College outcome. Capitol Police arrested just more than a dozen people the day of the breach while D.C. police arrested around 70. The DC Attorney's office is the largest federal attorney's office in the United States.
Rep. Peter Meijer, Michigan Republican, said, "It didn't have to be this way".
U.S. Transportation Secretary Elaine Chao and Education Secretary Betsy DeVos resigned on Thursday, joining a growing list of aides leaving Trump's administration in protest at the storming of the U.S. Capitol. The president told his supporters to "fight" to stop the "steal" of the election, while his personal lawyer, Rudy Giuliani, called for "trial by combat".
Pelosi is meeting with the House Democratic caucus Friday to consider impeachment proceedings against the president. Trump was later acquitted by the Senate on charges of abuse of power and obstruction of Congress over his dealings with Ukraine. Those being tried in federal court, where prosecutors can generally secure longer convictions, are charged with things like violent entry and disorderly conduct on Capitol grounds, assaulting a federal law enforcement officer and threatening House Speaker Nancy Pelosi.
On Saturday, New Jersey Gov. Phil Murphy ordered that the US and New Jersey flags be flown at half-staff at all state buildings and facilities in honor of Sicknick, saying he "embodied the selfless spirit of his native state".
Sicknick died "after defending the Capitol complex and protecting those who serve and work here".
Mr Sicknick's death brings to five the number of people who died due to the riot.
During his four years, Bicsko says Sicknick was well liked by the faculty, who described him as a steady worker, fine student and a nice young man.
"That was when it really started to get scary", said Wild, 63, describing Wednesday's dramatic siege of the complex that houses the US Congress. That section of the amendment has never been invoked.
He said that "these employers have to start realizing that reservists make up more than 50 percent of the military".
"A US Capitol Police officer has died from yesterday's riot".
Further, Biden said the uprising bordered on sedition, adding, "The scenes of chaos at the Capitol do not reflect a true America, do not represent who we are". It only mentioned that he collapsed after returning to the Division office.
As apparently premature news of Sicknick's death spread in law enforcement circles, the U.S. Capitol Police Department remained silent, including no response to an early request for confirmation from ProPublica on Thursday evening.