France and Germany, which are co-hosting the summit, have each deployed 15,000 police and troops in a security operation costing 110 million euros.
Demonstrators from as far as Japan have flocked to Strasbourg to campaign against war, defence spending and nuclear weapons.
Another group of protesters, who camped out overnight in central Strasbourg, are planning a demonstration later on Saturday.
Across the River Rhine, anti-war and anti-capitalist protest events have also been planned in the German towns of Kehl and Baden-Baden, where other summit events are taking place.
Hamish Macdonald, Al Jazeera's correspondent in Strasbourg, said: "The protesters are demanding a variety of things. Given that Nato is talking a lot about the war in Afghanistan there are a lot of people here voicing an anti-war message. Anarchist, socialist and green groups are also here.
"Some of the messages seem rather mixed and confused but I think the protests will continue throughout the day."
Police in Strasbourg had arrested hundreds of protesters before the summit opened on Friday.
Strasbourg's streets were virtually deserted throughout the day due to a tight security cordon that forbade unauthorised traffic in many parts of the city.
Schools and the university were closed and most businesses and restaurants have shut down for the duration of the summit.
Protesters at a campsite in Baden-Baden, who say their protests are peaceful, have criticised the police tactics.
"We have been treated like serious criminals," a German student at the campsite said.
"We were searched American-style with our hands on the car, but we are going to stay calm and we are not going to hit back."
Some protesters said they were frustrated by the large police presence in Strasbourg, Kehl and Baden-Baden, where Obama and Angela Merkel, the German chancellor, met for the summit's opening session on Friday.