Government ministers say new measures will make it easier to deport failed asylum seekers and tag extremists.
Anis Amri, 24, plowed a truck through a Berlin Christmas market on Dec. 19. Islamic State claimed responsibility for the attack.
Authorities suspect the 38-year-old migrant of seeking 180,000 euros ($189,000) from the Islamic State to fund one or more attacks.
Officials have redoubled efforts to prevent attacks like those in Germany and France this year in which suspected Islamic militants intentionally drove trucks into holiday crowds, killing dozens of civilians.
Anis Amri had contact with preacher Abu Walaa's network, a German security source tells Newsweek.
Angela Merkel's Bavarian allies want intelligence agencies to monitor people as young as 14.
Protection increased at the Vatican and near churches throughout Italian cities as authorities probe Anis Amri's connections within the country.
German authorities have issued a Europe-wide arrest warrant for Amri, 24.
It is harder to be cruel to someone with whom you have made a genuine connection.
Police raided an Islamic cultural center in western Berlin and arrested two men aged 28 and 48 at a separate location.