Heavy security was in place to prevent clashes between the two groups, with five police helicopters flying overhead to monitor the crowds.
Mainstream political parties and civic groups planned rallies to protest far-right attempts to exploit the city's painful history. Leaders of Germany's far-right fringe have in the past caused outrage by comparing the bombing of Dresden to the Holocaust.
Up to 7,000 far-right supporters from Germany and other European countries are expected, and at least 1,000 were already in the city, police spokesman Thomas Geithner said. Organizers have characterized the event as a "mourning march."
"The most important task for us is to keep both blocks separated and not to allow them any contact," Geithner said.
Mayor Helma Orosz said she hoped thousands would join a human chain symbolically protecting the restored city center from neo-Nazis. The city mounted an unsuccessful legal challenge to block the far-right march.
About 2,000 left-wing counter-demonstrators gathered Saturday morning a few hundred yards (meters) away from where the far-right was assembling, but there were no immediate signs of trouble. Many tried to block roads to prevent far-right supporters from reaching their assembly point.
Karolin Hanebuth, 20, came from Hannover in western Germany to counter the far-right protest.
"Fascism is not an opinion, it is a crime," she told The Associated Press.
The far right is marginal in Germany and has no seats in the national parliament. However, Saxony, where Dresden is located, is one of two eastern German states where the far-right National Democratic Party has seats in the regional legislature.
Three successive waves of British and U.S. bombers on Feb. 13-14, 1945, set off firestorms and destroyed Dresden's centuries-old baroque city center.
The total number of people killed in the Dresden bombing has long been uncertain. In 2008, a panel commissioned by state officials found that the firebombing killed no more than 25,000 people
- far fewer than scholars' previous estimates that ran as high as 135,000.
Dresden has been rebuilt painstakingly over the years. Its landmark domed Frauenkirche, or Church of Our Lady
- for decades no more than a mound of rubble - reopened in 2005.