Frederiksen made the comments in an interview with newspaper Berlingske as her government prepared to announce new public security proposals on Thursday.
A series of minor explosions in Copenhagen this summer, several of which have been linked to gang crime, are connected to the measure.
The government is to propose “significantly” more police surveillance in the form of 300 new security cameras, which law enforcement will be able to install at its own discretion.
That could mean a lot more cameras pointed at public buildings.
Under current law, public spaces which are freely accessible may not be monitored by cameras.
The PM said she wants that to change, enabling the police to “watch broadly and not just narrowly”.
Overall, the measure constitutes a major change in Denmark‘a approach to public surveillance, the prime minister admitted.
“We are now going very far with an expansion of surveillance, because it has proven to be a very useful resource,” she said to Berlingske.
Additional measures in the proposal include tougher punishments for possession of explosives, better protection of the border with Sweden and bolstered police investigations.
Police suspect individuals who travelled from Sweden of carrying out a bombing at the Tax Agency in Copenhagen in August.
Frederiksen noted that 13 explosions have occurred this year in Copenhagen, and that as many as 180 gang members were convicted of crimes in the first seven months of 2019.
“This is not going to just go away, and that’s why we need to take drastic steps,” she told Berlingske.