The Berlin minister in charge of security, Andreas Geisel, also alleged there had been a police cover-up later as the Berlin State Criminal Investigation Department had sought to deflect blame.
Geisel said he had launched a criminal complaint against persons unknown inside the department.
Tunisian Anis Amri, 24, hijacked a truck on December 19th, killed its Polish driver and ploughed the vehicle through the market, claiming 11 more lives and wounding dozens.
He was shot dead by Italian police while on the run in Milan, four days after the attack which was claimed by terror group Isis.
In the aftermath of Germany's bloodiest jihadist attack, officials admitted a series of security failures that allowed Amri to register under multiple identities and evade authorities while he was in contact with Islamist militants.
Amri, a failed asylum-seeker who had previously served jail time in Italy, should also have been deported months earlier, but it emerged Tunisia had not provided the necessary paperwork until after the attack.
He had been under surveillance since March 2016 in Berlin, but security services said they dropped their watch in September, having only observed his activities as a drug dealer.
Geisel has now said police knew he was not just a small-time drug dealer as first claimed but had engaged in commercial-scale, organised drug trafficking, for which he said police could have obtained an arrest warrant.
Geisel also alleged that one or more police involved had later forged a document in the cover-up of the omission.
A file mentioning that Amri had dealt with only small quantities of illegal drugs was apparently written on January 17th but backdated to November 1st, he said.