Hundreds of officers in riot gear are patrolling the area near the disputed youth centre than has been at the heart of the violence.
More than 500 people, including scores of foreigners, have been arrested in riots that started on Thursday after an anti-terror squad evicted squatters from a disputed youth centre in the city's Noerrebro district.
Of these, around 200 were arrested early on Saturday following overnight clashes where hundreds of protesters hurled cobblestones at riot police who responded with tear gas.
During the violence a school was vandalised and several buildings were damaged by fire as flames spread from burning cars and trash bins.
One protester was reportedly wounded, while 25 were injured in riots the night before in what police called Denmark's worst riots in a decade.
Peter Vesterheden, head of Copenhagen prison's, said jails in the city were filling up, with 115 people remanded into custody, including 25 foreigners.
Jan, a 22-year-old activist Jan, said: "This is a display of anger and rage after more than seven years of struggle to keep what is ours," adding that he had been coming to the building for 10 years.
On Saturday afternoon, 3,000 demonstrators marched peacefully toward building as hundreds of police followed the procession from a distance and sealed off streets in the immediate area.
Copenhagen residents had mixed feelings about the demonstrations.
As she watched Saturday's demonstration pass by, Berit Larsen, 57, said: "The idea of an alternative society is good. We need to have room for everyone but the violence we have seen is not what I consider an alternative way for society."
The protesters see their fight to keep the "Youth House," a four-story building used by young squatters since the 1980s, as symbolic of a wider struggle against a capitalist establishment.
Built in 1897, it was a community theatre for the labour movement and a culture and conference center.
Vladimir Lenin was among its visitors while in recent years it has hosted concerts with performers including Australian musician Nick Cave and Icelandic singer Bjork.
The eviction had been planned since last year, when courts ordered the squatters to hand the building over to a Christian congregation that bought it six years ago.
The squatters refused to leave, saying the city had no right to sell the building. They have demanded another building for free as a replacement.
As news of the riots spread, sympathizers around Europe rallied support for the protesters.
Demonstrations were held in Hamburg, northern Germany, and in Norway, Sweden and Finland.