The gunman, known to security services, is on the run and is being hunted by police. "He fought twice with our security forces," said Interior Minister Christophe Castaner.

The shooting happened close to a Christmas market near one of the central squares, Place Kléber.

France's counter terrorism prosecutor has opened an investigation.

Six of the injured are said to be in a serious condition, while six others suffered light injuries, police said.

Confirming that three people had died, Mr Castaner said that border controls had been strengthened, with 350 security agents hunting for the gunman.

He added that security at all Christmas markets would be stepped up.

Police said the 29-year-old suspect was born in Strasbourg and was already known to the security services as a possible terrorist threat.

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 have been urged to stay indoors amid unconfirmed reports he has 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.

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