Petermann said, however, that his freedom of movement within the European Union had been removed.
Three people were killed and 12 others injured.
On Tuesday morning, before the attack, authorities in Strasbourg visited Chekatt's home to arrest him on suspicion of homicide.
Interior Minister Christophe Castaner said the suspected attacker was "notorious" and has an extensive criminal record.
At Chekatt's apartment, in an outer neighborhood of Strasbourg, the lock of the door was broken at his apartment.
"The government has made a decision to move the security level to 'Emergency Attack" with stricter controls at the borders, and the implementation of reinforced controls on all the Christmas markets that are taking place in France to avoid the risk of copycat attacks'.
Two people died in the attack and another was declared brain dead, Paris prosecutor Remi Heitz said.
A further revelation came from a neighbour, speaking to the Associated Press on condition of anonymity, who said she saw Chekatt, who she said was rarely at home, speaking to an unknown man in the hallway on Monday, the day before the attack. He also left 12 people injured.
Mr Castaner said: "Three hundred and fifty police and gendarmes are now on the ground to apprehend the suspect, supported by two helicopters, the RAID (French anti-terror police), the BRI (anti-gang brigade) and the Sentinel force". There, he exchanged more gunfire with police and disappeared. They had wanted to take him into custody as in an investigation for suspected murder.
The official could not be identified because he was not authorized to disclose details on the investigation.
The parliament is now in plenary session, with hundreds of MEPs and officials having made the monthly visit to Strasbourg from Brussels. The European Parliament was also in session in Strasbourg, adding to the crowds in the city.
"One of them fell down, I don't know whether it was because she was tripped up or if she was hit", the witness said. "We have to go forward and not change our ways", Tajani said.
The 2016 court verdict in the southern German city of Singen, obtained by the AP, said he was sentenced to prison in France in 2008 and in Basel, Switzerland, in 2013 for various robberies. News agency dpa reported that he was deported to France in 2017. The Ministry is in contact with the local authorities and is keeping an eye on the situation in Strasbourg.
From there he could take a train to cross the French-German border in just 5 minutes, reaching the German town of Kehl.
French security forces are trying to catch the suspected Strasbourg gunman dead or alive, as the city in eastern France mourned with flowers and lit candles left at the site of the attack near its famous Christmas market. At least 13 people were wounded, several of them critically.
Local authorities, meanwhile, increased the death toll in the attack to three. The office said the man is a member of the "entourage" of Chekatt but not a family member.
The office of the Paris prosecutor said it was investigating a terrorist murder and attempted murder. In addition to the approximately 350 military personnel searching for shooter are 100 judicial police officers, two helicopters and a special forces team, Castaner said.
Authorities say the 29-year-old was known to have developed radical religious views while in jail.