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.
The shooting happened close to a popular Christmas market near one of the central squares, Place Kléber.
France’s counter-terrorism prosecutor has opened an investigation.
There were reports on Wednesday morning that a police operation had been launched around the cathedral area in the city.
The motive for the shooting remains unclear.
“He fought twice with our security forces,” French Interior Minister Christophe Castaner said.
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Image caption Armed police secure the area after the deadly shooting incident on Tuesday
Confirming that three people had died, Mr Castaner said that border controls had been strengthened and security at all Christmas markets would be stepped up, with 350 security agents hunting for the gunman.
He added that France had raised its security alert level to “emergency attack”.
Six of those reportedly injured on Tuesday were said to be in a serious condition, while six others suffered light injuries, police said.
Police added that the 29-year-old suspect was born in Strasbourg and was already known to the security services as a possible terrorist threat.
Image copyright ANADOLU AGENCY/GETTY IMAGES
Image caption Police searched the narrow streets near the Christmas market in Strasbourg
According to France’s BFM TV the man had fled his flat in the Neudorf district of the city on Tuesday morning as it was being searched by police in connection with a robbery.
Grenades were found during the search.
Residents in Neudorf were urged to stay indoors following unconfirmed reports that the suspect had been tracked down and cornered by police in the area.
The European Parliament, which is nearby, was placed on lockdown. The parliament’s president, Antonio Tajani, tweeted to say it would “not be intimidated by terrorist or criminal attacks”.
French President Emmanuel Macron, who had attended a crisis meeting with cabinet officials in Paris, later tweeted that the “solidarity of the entire nation” was with Strasbourg, the victims and their families.
Panic in the city
The attack unfolded at around 20:00 local time (19:00 GMT) close to Strasbourg’s famed Christmas market, which attracts thousands of visitors at this time of year.
Eyewitness Pater Fritz told the BBC he heard gunfire and found a person who had been shot, lying on a bridge. He said he tried to resuscitate him but the man died.
“There are no ambulance services able to enter the area, apparently,” he said, adding: “After 45 minutes we stopped the resuscitation [attempt], because a doctor told us on the phone that it was senseless.”
Another eyewitness, who gave his name as Fatih, told AFP news agency that after the shots were fired there was “pandemonium” on the streets.
“People were running everywhere,” he said.
Local journalist Bruno Poussard wrote on Twitter that there had been a dozen shots fired on his street in the city centre – one or two to begin with, then in bursts.
Emmanuel Foulon, a press officer for the European Parliament, wrote that there was “panic” in the centre following the sound of gunfire and that police with guns were running through the streets.
A shopkeeper told BFM TV: “There were gun shots and people running everywhere. It lasted about 10 minutes.”
British MEP Richard Corbett tweeted that he was in a restaurant in the city and the doors had been locked.
The mayor of Strasbourg, Roland Ries, later tweeted that the Christmas market would be closed on Wednesday following events. He added that flags would be lowered to half-mast at the local Town Hall, where people could pay their respects in a book of condolences.
Strasbourg Christmas market. This very place as seeing a stunning site with a stunning night is where the incident went on when the telorist targeted
Due to the violence that occurred led the police into sleepless night
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