Video televised by WLS-TV, Chicago, showed police striking protesters with batons.
Occupy Chicago, an organizer of the demonstrations -- intended primarily to protest the Afghan war -- wrote on its Twitter page that police had "several demonstrators detained behind their lines, calling for medics. Bloodied protesters being dragged out of sight now."
A Chicago city official, speaking off the record, told CNN protesters identified as aggressors were "extracted" after an estimated 50-75 protesters threw objects at police and refused to leave the area.
The confrontation began around 5 p.m. and most of the crowd had left the area by 6:45, WLS said.
"There will be great challenges ahead," Obama said. "The loss of life continues in Afghanistan. There will be hard days.
"But we are confident we are on the right track and (what) this NATO summit reflects is that the world is behind the strategy we've laid out. Now it's our task to implement it effectively and I believe we can do so in part because of the tremendous strength and resilience of the Afghan people."
Thousands of protesters converged on Chicago's Grant Park for a noon rally at the Petrillo Music Shell, with some waving signs calling for U.S. troops overseas to be brought home, the Chicago Tribune reported. The newspaper said the police presence was large to keep the demonstration peaceful.
Thousands of the protesters began marching toward McCormick Place, west on Jackson, south on State, east on Harrison and south on Michigan, led by war veterans, the Chicago Sun-Times said.
Some of the veterans, many dressed in camouflage, planned to return their war medals in a ceremony on McCormick, the Sun-Times said.
Chicago Police Superintendent Garry McCarthy told a news conference at the edge of the park that "99.9" percent of protesters have listened to police direction, the Tribune reported.
McCarthy predicted demonstrations would be peaceful Sunday.
The organizers of rally and march to the summit venue at the massive McCormick Place convention center have the necessary city permits, but police officials said they expected some participants to break off and confront officers as they have repeatedly in recent days.
As many as 1,000 anti-war and anti-NATO protesters paraded through the city Saturday and were corralled away from the city's high-end Michigan Avenue retail district, where most of the NATO dignitaries are staying, the Tribune said.
Sunday's rally was expected to be the largest held during the summit. WBBM in Chicago said about 700 people were on site by the mid-morning. Most of them were under shade trees as the temperature poked into the 80s.
Organizers said they expected their supporters to behave themselves, but also ignore what they said were veiled warnings by the city to stay clear of downtown.
"Our fear has been that people would listen to the messages of fear from local leadership, but I think people are going to turn out in spite of that," protest organizer Andy Thayer told WLS-TV, Chicago.
One potential hitch in the turnout was the announcement that a charter bus company would not be providing shuttle service for the protesters staying around Chicago. The company said its drivers had worked too many hours and were being grounded for mandatory rest period, WBBM said.