Strasbourg, France (CNN) On Thursday French police evacuated buildings and cordoned off the area where a lone gunman fled after he killed at least three people and wounded 13 others on Tuesday at a Christmas market in the eastern city of Strasbourg.

A spokeswoman for the Interior Ministry told CNN that it was an operation that involved "conducting checks."

Since the shooting, authorities have described Tuesday's incident as a terrorist attack.

Members of the French police special forces take part in an operation at the Neudorf neighborhood in Strasbourg.

The suspect, identified as 29-year-old Cherif Chekatt, has an extensive criminal background that includes 27 convictions in France, Germany and Switzerland, mainly for acts of robbery and violence.

On Tuesday more than 700 police and military officers across three European countries joined the hunt on Tuesday for Chekatt.

Swiss police said they were "on alert" and in close contact with their French counterparts, while Germany's federal police said they were conducting intensive search efforts on roads and railways, which could cause delays for people crossing the border. French anti-terror police have also joined the search, as efforts stretch into a second day.

Cherif Chekatt

A curfew in the eastern French city, which lies on the border with Germany, has been lifted but law enforcement urged vigilance. Border security has been tightened and a perimeter was set up around Strasbourg, but authorities on Wednesday were unsure if the suspect was still in France.

Strasbourg police said Thursday that the suspect had killed three people and injured 13 -- including five seriously and eight who were suffering from minor injuries.

The suspected shooter was known to prison officials for being radicalized and for his proselytizing behavior in detention in 2015, Paris prosecutor Remy Heitz said, adding that he had been incarcerated multiple times in the past.

French prosecutors said the suspect shouted the Arabic phrase "Allahu Akbar," meaning "God is greatest," at the time of the attack.

The man was already known to security services as a possible threat, police said.

The father, mother and two brothers of the suspect are in custody and being questioned by police, a source close to the investigation told CNN.

French special forces search a bank of the River Rhine in Strasbourg on Wednesday as they hunt the gunman.

The attack prompted France to raise its national security threat level to its highest "emergency terror attack" status.

"What happened last night is unquestionably an attack, a form of terrorist attack," Strasbourg Mayor Roland Ries told CNN by phone on Wednesday.

Police carry out checks on the border between Germany and France in Kehl, southern Germany, on Wednesday.

Suspect injured in exchange of fire

Strasbourg's famed Christmas Market is one of the oldest in Europe and draws millions of visitors each year. The suspect entered the perimeter of the market by the city's Corbeau Bridge, and began shooting at passers-by on the Rue des Orfèvres at about 8 p.m. local time, when many were in the middle of their Christmas shopping.

Anti-terror police descended on the market and attempted to apprehend the suspect as he traversed several streets. He exchanged fire with security forces, suffering an injury to his arm. "Throughout this journey, he repeatedly opened fire with a handgun and used a knife which he both used to seriously injure and kill," said Heitz, speaking in Strasbourg.

The suspect then fled the scene by a taxi and headed to the city's Neudorf district, the Paris prosecutor's office said. Heitz had earlier said the destination was Neuhof, a more distant district of Strasbourg.

"The taxi driver stated that he had seen him in possession of a handgun and he had injuries," said Heitz. The man again exchanged fire with police after leaving the taxi, he added.

The counter terror section of the Paris prosecutor's office has opened an investigation for murder in connection with a terrorist enterprise, and attempted murder in connection with a terrorist enterprise, said Heitz.

Gunman was known to police

The suspected gunman, who was previously identified by CNN affiliate BFM as a 29-year-old male born in Strasbourg, was on a French watch list called a "Fiche S" surveillance file.

The "Fiche S" is a French terror and radicalization watch list that includes thousands of people, some of whom are under active surveillance, meaning they are on law enforcement's radar.

French gendarmes had attempted to bring him in for questioning Tuesday morning before the attack but found he wasn't home, a spokesperson for France's National Police told CNN, without providing further details.

French police officers stand guard near the scene of the shooting on Tuesday.

The interior ministry in the German state of Baden-Wuerttemberg confirmed Wednesday that the suspect had been convicted of break-ins and serious theft by a court in Singen in 2016 and subsequently spent time in a prison in the city of Freiburg. He was deported to France in 2017.

The German authorities cooperate closely with their French partners, a spokesman for the interior ministry said, adding that it cannot be ruled out that the suspect may have crossed the open border. Swiss officials also said they were on alert.

The German Federal Criminal Office said the suspect was not known in Germany as a radical Islamist.

A spokeswoman for the Swiss Federal Police, Cathy Maret, told CNN the alleged attacker was well known to authorities there, having been arrested and convicted several times in Switzerland for crimes such as break-ins, theft and violence. He was not on their radar as a radical Islamist or for narcotics violations, she said.

Witness: 'It was a moment of terror'

Simone Ceruti was in the city's Kleber Square when the shooting started. "There was a lot of panic, people fleeing and seeking for shelter," said Ceruti, who filmed footage of the police response from a nearby apartment.

"I let a few ladies in the building where I'm staying these days and then they were accompanied by police," he said. "It was a moment of terror."

The injured were taken to a Strasbourg hospital.

French President Emmanuel Macron tweeted early Wednesday in solidarity with the French people. "Solidarity of the whole Nation for Strasbourg, our victims and their families," he said

In a tribute to the victims of the shooting, the Eiffel Tower in Paris went dark at midnight local time.

The Eiffel Tower goes dark on December 13, 2018.

The Christmas market was closed Wednesday and flags were flown at half-staff.

All rallies and demonstrations throughout the Strasbourg area were barred until further notice, the Prefecture of the Grand East and Lower Rhine Region said.