The protest march by the right wing Party of the Swedes (Svenskarnas party - SVP) attracted a large police presence, reckoned to be as high as 450 officers, following trouble at a similar rally last year.
In addition to the 19 arrests, a further 90 people were taken away from the scene by bus. Another 32 people were taken into custody on grounds of causing disorder. It's understood that of the 19 arrests, 13 of them were as a result of disobeying police orders.
Two people were left injured while a right wing demonstrator was also arrested after a clash.
The demonstration was briefly stopped as counter demonstrators blocked the protest route before it finally got underway. By 5pm the scene was described by police as relatively calm as the planned demonstration by the neo-Nazis was conducted.
"Can't say that it will last forever but right now the situation is stable," police spokesman Lars Byström told the TT news agency.
Byström added that the police surrounded the protesters as they were attempting to disturb a licensed demonstration.
"We took some into temporary custody to get control over the situation," he said.
Earlier in the day police carried out a controlled demolition of a suspicious package found close to the route of the march.
Last year's march hit the headlines after five people were left injured and scores were detained after extreme-left demonstrators attacked a similar march carried out by the SVP party.