The plan, mooted before the weekend shootings, will enable the intelligence services to better monitor Danes travelling abroad to fight with the Islamist State group, while also targeting the radicalisation of prisoners in jails.
"We want to strengthen our ability to gather and analyse (information) about terror planning abroad," Prime Minister Helle Thorning-Schmidt told a briefing.
"We want to ensure that the intelligence service is able to monitor Danes who travel abroad to take part in extremist activities."
A total of 110 Danes have travelled to Syria to fight in the civil war, making the country the second largest source per capita of European jihadist fighters in the Middle East, after Belgium.
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Many are believed to have returned home afterwards.
The country has been left in shock after the shootings in Copenhagen which targeted a meeting on free speech and Islam and the capital's main synagogue.
The suspected gunman, a 22-year-old Dane of Palestinian origin identified as Omar El-Hussein, was shot dead by police early on Sunday.