At least two people have been killed and 11 others injured in a shooting in an attack in the eastern French city of Strasbourg.

The lone gunman, known to security services, is on the run and is being hunted by police.

French authorities are treating the shooting as a terrorist act after identifying the gunman, named Cherif C, a radicalised 29-year old from the city on a “S” security and terror watch list.

He had been injured in an exchange of gunfire with a soldier.

The mayor of Strasbourg reportedly said that four had died.

Seven of the injured and were said to be in a serious condition.

Police said the shooter started his attack in the city centre just before 8pm where the celebrated Christmas market, which attracts millions of tourists every year, was taking place.

The anti-terrorist section of the Paris prosecutor’s office declared the incident to be an act of terrorism and announced an inquiry had been opened into “murder and attempted murder in relation to a criminal enterprise”.

The Herald:

The Christmas market has been the target of threats from Islamist extremists in the past.

Confirming the death toll, the French interior minister, Christophe Castaner, who is on his way to the city, called it a "serious public security incident".

Witnesses said the gunman had fired a first volley of rounds near the market around 8pm then a second a few metres further on.

Security officials have cordoned off the area around the Christmas market and trams have been stopped, according to reports.

Residents in the Neudorf and Etoile park districts have been urged to stay indoors while the hunt for the gunman continues.

“There were gunshots and people running everywhere,” said one shopkeeper. “It lasted about 10 minutes.”

A restaurant waiter told how staff and customers tried to save a diner who stepped outside and was shot. “We used napkins to try to stem the blood.” He said the man had died.

Theresa May said she was "shocked and saddened" by the "terrible" attack in Strasbourg. She tweeted: "My thoughts are with all of those affected and with the French people."

Police confirmed the gunman, aged 29, and born in Strasbourg, is on the national “Fiche S” list of people considered a potential security risk.

Some 26,000 individuals suspected of posing a security risk to France are on the Fiche S watch list, of whom about 10,000 are believed to have been radicalized, sometimes in Salafist mosques, online or abroad.

Strasbourg is home to the European Parliament, which is currently hosting a meeting of European leaders, was put on lockdown, and the parliament’s safety awareness division sent a message to MEPs advising those dining in the city centre to “please stay inside and don’t go out”.

“[A] decision has been taken, as a precautionary measure, to close the European Parliament building in Strasbourg. We ask you to stay calm and safe within [European parliament] premises,” it read.

Officers said he had shot at soldiers patrolling as part of the nationwide Operation Sentinelle, reportedly injuring one of them.

Sentinelle is a French military operation introduced in the aftermath of terrorist attacks in and around Paris in January 2015.