Protests against the incoming Biden government had been planned for several weeks in all US states on Sunday.
Authorities feared new violence, but Sunday was calm.
Dozens of states had called in the National Guard to protect their state congressional buildings, but in the vast majority of places, police, soldiers and the National Guard were many times more than the demonstrators.
"It was a non-incident today and we are happy about it," Troy Thompson, a spokesman for the authority responsible for the protection of the Pennsylvania Capitol in Harrisburg, told Reuters.
Only a few protesters had gathered there, and they are said to have dispersed before dark.
In Virginia's capital Richmond, only soldiers and a few journalists are said to have appeared on the streets.
The threat remains
Groups of armed protesters, on the other hand, are reported to have gathered at state conventions in Ohio, Michigan, Oregon and Texas, among others, but no violence is said to have broken out.
It is unclear how much the presence of security personnel and the FBI's warnings affected the demonstrations.
According to Reuters, several right-wing extremist groups have warned their members about increased security and that the police were trying to lure them into a trap.
However, the threat of demonstrations remains for the week, when Joe Biden on Wednesday will be installed as the 46th president of the United States.
About 10,000 soldiers from the National Guard are on site and the day before Biden is sworn in, further reinforcements are expected.
The many soldiers characterize the cityscape in the capital.
The Washington Post reports that almost only camouflage-clad armed forces are visible on the streets and that only military vehicles are allowed to operate in central Washington DC.