Mr. Gieswein, who runs a private paramilitary training group called the Woodland Wild Dogs, was among the early wave of invaders to breach the Capitol, court papers said. Photographs from the attack show him clad in a military vest, goggles and an Army-style helmet, wrestling with Capitol Police officers to remove metal barricades and brandishing a baseball bat. In a criminal complaint, prosecutors cited a video of Mr. Gieswein encouraging other rioters as they smashed a window at the Capitol with a wooden board and a plastic shield and then climbing through the broken glass into the building.

Mr. Gieswein was photographed inside the building with another suspect, Dominic Pezzola, a former Marine and member of the Proud Boys, who was charged last week.

After the assault, Mr. Gieswein said in a news documentary interview that he attacked the Capitol to “get the corrupt politicians out of office,” according to court papers, adding, “They have completely destroyed our country and sold them to the Rothschilds and Rockefellers.”