Police spokesman Kjell Lendgren said around 400 leftists had gathered to heckle the 100-strong demonstration, which was rallying to bring attention to what it perceives is the Islamization of Europe.
He said the leftists shouted and blew vuvuzelas to drown out anti-Islam and nationalist speeches, but then started throwing bottles and lit fireworks at police, injuring two officers.
Lendgren said ten activists were arrested, after which the situation calmed down.
Both the anti-Islam meeting and leftist protest continued peacefully and were scheduled to end at 1600 local (1400GMT).
Nationalist groups such as the English Defence League were instrumental in organizing the anti-Islam event, which was described on the anti-Islam European Freedom Initiative's website as the "first worldwide counter-jihad action."
In the counter protest, local activists called for tolerance and warned of a rise in fascism. They referred to the nationalist groups as "Breivik's foot-soldiers"—a reference to Norwegian ultra-nationalist Anders Breivik who killed 77 people in Norway last year.