Germany has proposed stripping dual nationals who fight for extremist groups abroad of their citizenship.
And interior minister Thomas de Maiziere wants to make it easier to deport foreigners deemed to be dangerous.
Mr de Maiziere's list of proposals aimed at beefing up security in Germany following a recent string of attacks also included making "promoting terrorism" a criminal offence, and considering further reinforcements for security forces.
In addition, Germany will consider joining other countries in screening the public social media profiles of people being admitted to the country under humanitarian resettlement programmes.
Mr de Maiziere also wants to strengthen German authorities' ability to probe the "darknet", an area of cyberspace invisible on the open internet.
The minister proposed making it easier to take foreigners who have committed crimes or otherwise are deemed to be dangerous into pre-deportation custody, making "endangering public security" a ground for jailing them.
The move is meant to make it easier to ensure people who are obliged to leave the country actually do so.
Two of the attacks in a week-long period starting July 18 - an axe rampage near Wuerzburg that wounded five and a suicide bombing that injured 15 outside a bar in Ansbach - were the first in Germany to be claimed by the so-called 'Islamic State' group.
Both of the attackers, asylum-seekers who arrived over the past two years, were killed.
In two other attacks - a shooting by a German-Iranian 18-year-old in Munich that claimed 10 lives, including the assailant's, and the stabbing of a woman by a Syrian asylum-seeker at a restaurant in Reutlingen - the motive is still unclear but Islamic extremism is not suspected.
The attackers in Ansbach and Munich had received psychiatric treatment in the past.
Mr de Maiziere said the government will discuss with doctors ways to "minimise dangers to citizens as far as possible", but stressed that patient confidentiality rules will be upheld.
In Germany, doctors can face a fine or up to a year in prison for breaching patient confidentiality, though existing rules already allow them to do so "in order to safeguard a higher-ranking legally protected interest".
Some members of Chancellor Angela Merkel's and Mr de Maiziere's conservative party have called for further measures - such as a ban on all-body veils worn by some Muslim women.
Mr de Maiziere made it clear, however, that such a ban is "constitutionally problematic" and is not on the cards.
"You can't ban everything that you reject," he added.