A union chief says civilians are “outraged and anxious” that security services stopped tracking the main suspect.
A Europe-wide manhunt is under way for the main suspect in the Berlin lorry massacre amid questions over how he was able to evade intelligence agencies.
Anis Amri, a Tunisian asylum seeker who was known to police, is thought to be armed.
He is suspected of being at the wheel of a hijacked 25-tonne lorry which ploughed into a crowd of shoppers at a busy Christmas market.
German officials said the 24-year-old came to their attention in March after a tip-off that he might be planning a robbery to raise money for automatic weapons to use in an possible attack.
They followed him until September, when it was decided there was no evidence to back up the original suspicions. He then fell off the radar.
Rainer Wendt, the head of a union representing German police, said civilians are “rightly outraged and anxious that such a person can walk around here, keep changing his identity and the legal system can’t cope with them”.
Meanwhile, German newspaper Der Spiegel criticised authorities who “had (Amri) in their crosshairs and he still managed to vanish”.
On Wednesday, it was reported that police searched a refugee centre in Emmerich, west Germany, where Amri stayed a few months ago, as well as two apartments in Berlin.
Prosecutors warned the suspect could be armed and dangerous and have offered a €100,000 (£84,000) reward for information leading to his arrest.
Twelve people were killed and 48 others injured in Monday evening’s attack, which has been claimed by the Islamic State terrorist group.
Amri is described as being 5ft 8in tall, with black hair and brown eyes.
He is thought to have used six different aliases and three different nationalities.
Anti-terror police have questioned Amri’s family, who live in the town of Oueslatia, north Tunisia.
Abdelkader Amri, his brother, said he was “in shock”.
“(I) can’t believe it’s him who committed this crime,” he told the AFP news agency.
“If he’s guilty, he deserves every condemnation.
“We reject terrorism and terrorists – we have no dealings with terrorists.”
Amri’s father told a radio station his son had left Tunisia seven years ago as an illegal immigrant.
He was accused of violent robbery in his home country and served four years in an Italian prison over allegations he was involved in burning down a school, according to reports.