Some were seen taking pictures of the monuments and taking a break on the steps that were occupied by rioters last week.
Another 10,000 will arrive on Saturday as the FBI warns of the risk of more violence from armed extremists holding pro-Trump events in 50 state capitols between now and inauguration next week.
Washington DC Mayor Muriel Bowser is urging people to avoid coming to the city for Joe Biden's presidential inauguration on 20 January.
She says people should participate virtually instead.
