Eyewitnesses described what they saw, as the shooting unfolded near a Christmas market in the eastern French city.
French Interior Minister Christophe Castaner says hundreds of people had been deployed to hunt the killer.
The suspect, who is known to security services, escaped after exchanging fire with soldiers and armed police on Tuesday. He is believed to be injured.
Police say the 29-year-old suspect was born in Strasbourg and was already known to the security services as a possible terrorist threat.
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