Police said video surveillance indicated the man was behind both killings, one which took place at a panel discussion about Islam and free speech, and the other outside Copenhagen's main synagogue.
"We are still investigating whether he acted alone," police spokesman Jorgen Skov says.
Torben Moelgaard Jensen later told a press conference: "We believe the same man was behind both shootings and we also believe that the perpetrator who was shot by the police action force at Noerrebro station is the person behind the two attacks."
Lars Vilks, the Swedish cartoonist whose controversial caricatures of the Prophet Mohammed sparked worldwide protests in 2007, had been among the speakers at the Krudttoenden cultural centre when a man opened fire.
A 55-year-old man was killed when the gunman sprayed bullets at the cultural centre, while a young Jewish man was gunned down outside the synagogue.
The synagogue attack took place in the Krystalgade area, with two police officers also shot in the arm and leg and the gunman fleeing from the scene on foot.
A manhunt was already under way for a terrorist shooter who opened fire at an event at a Krudttonden cafe, leaving one person dead and three police officers injured.
In the cafe attack police said Vilks and French ambassador to Denmark Francois Zimeray were both unharmed.
Danish prime minister Helle Thorning-Schmidt told reporters: "We feel certain now that it's a politically motivated attack, and thereby it is a terrorist attack.
"We take this situation extremely seriously. We are in a high alarm all over the country, and our main priority at this stage is to catch the perpetrators and make sure that we find them as soon as possible."
Prime Minister David Cameron said his thoughts were with the Danish people, tweeting: "I condemn the shootings in Copenhagen.
Freespeech must always be protected."
The cafe in Copenhagen was hosting an event titled Art, Blasphemy And The Freedom Of Expression when the shots were fired, according to reports.
It comes little more than a month after the attack on the offices of the French satirical magazine Charlie Hebdo in Paris which left 12 people dead.
According to larsvilks.com, the event was marking the anniversary of the fatwa against Salman Rushdie.
Jodie Ginsberg, chief executive of Index on Censorship, condemned the Copenhagen attacks, saying: "The use of violence on a gathering exploring the intersection of religious and artistic freedom should send shivers down our spines.
"It would be terrible if violent acts such as that in Copenhagen shut down free speech even further."
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