The proposed measures include extending the period that people can be detained before deportation, making extremists wear electronic ankle monitors and withholding foreign aid to countries who fail to take their citizens back.
The announcement came less than a month after 12 people were killed and dozens more were injured when a 24-year-old Tunisian man drove a truck into a busy Christmas market in Berlin.
Chancellor Angela Merkel said that the December 19 attack, claimed by the Islamic State group, demanded a swift response that guaranteed both security and civil liberties.
Amri, who had used at least 14 different identities since coming to Germany in 2015, had also been on authorities' radar as a potential security risk.
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Justice Minister Heiko Maas told reporters in Berlin that the government intended to do "everything to prevent a repeat of the Amri case."
Asylum-seekers who try to hide their real identity will be required to reside in a specific jurisdiction in future, according to the proposals thrashed out by Maas and Interior Minister Thomas de Maiziere.
"It's always better to prevent radicalization than to have to find, convict and jail radicals who have committed crimes," Maas said.
Some of the measures will require parliamentary approval.
Public debate about domestic security has intensified following last month's attack, with all political parties toughening their stance before a general election expected in September.
Maas and de Maiziere belong to the center-left and conservative parties, respectively, in Merkel's "grand coalition" of traditional rivals.