A Danish film maker attending a panel discussion on blasphemy was killed in the shooting Saturday at the free speech event and a member of the Scandinavian country's Jewish community was killed outside the synagogue. Five police officers were also wounded in the shootings.
Police believe the suspect carried out both shootings alone but were investigating whether he had received help from others.
"Denmark has been hit by terror," Danish Prime Minister Helle Thorning-Schmidt said. "We do not know the motive for the alleged perpetrator's actions, but we know that there are forces that want to hurt Denmark. They want to rebuke our freedom of speech."
Jens Madsen, head of the Danish intelligence agency PET, said investigators believe the gunman was inspired by Islamic radicalism.
"PET is working on a theory that the perpetrator could have been inspired by the events in Paris. He could also have been inspired by material sent out by (the Islamic State group) and others," Madsen said.
Islamic radicals carried out a massacre at the Charlie Hebdo newsroom in Paris last month, followed by an attack on Jews at a kosher grocery store, taking the lives of 17 victims.
Earlier Sunday, at least two people with handcuffs were taken out by police from an Internet cafe in Copenhagen, Danish media reported. Police spokesman Steen Hansen told The Associated Press that "the action was part of the police investigation" but declined to give further details.
The Danish Film Institute said the 55-year-old man killed at the free speech event was documentary filmmaker Finn Noergaard.
The institute's chief Henrik Bo Nielsen said he was shocked and angry to find out Noergaard was gunned down while attending a discussion on art and free speech.
Noergaard directed and produced documentaries for Danish television, including the 2004 "Boomerang boy" about an Australian boy's dreams to become a world boomerang champion and the 2008 "Le Le" about Vietnamese immigrants in Denmark.
Denmark's Chief Rabbi, Jair Melchior, identified the Jewish victim as Dan Uzan, 37, a longtime security guard for the 7,000-strong community. He was guarding a building behind the synagogue during a bat mitzvah when he was shot in the head. Two police officers who were there were slightly wounded.
Israel's Prime Minister Benjamin Netanyahu decried the attack and said his government plans to encourage a "massive immigration" of Jews from Europe.
"Again, Jews were murdered on European soil just because they were Jews," Netanyahu said at the start of his Cabinet meeting Sunday. "This wave of attacks is expected to continue, as well as murderous anti-Semitic attacks. Jews deserve security in every country, but we say to our Jewish brothers and sisters, Israel is your home."
Other leaders also condemned the attacks, including British Prime Minister David Cameron, German Chancellor Angela Merkel and EU President Donald Tusk,
"The shootings in Copenhagen are an appalling attack on free speech and religious freedom," Cameron said. "Two innocent people have been murdered simply for their beliefs and my thoughts are with their loved ones and all those injured at this tragic time."
The first shooting happened before 4 p.m. Saturday when the gunman used an automatic weapon to shoot through the windows of the Krudttoenden cultural center during a panel discussion on freedom of expression featuring a Swedish artist who had caricatured the Prophet Muhammad. The artist, Lars Vilks, was whisked away unharmed by his bodyguards, but Noergaard was killed and three police officers were wounded.
The attack at the synagogue occurred hours later, shortly before 1 a.m. Sunday.
About four hours later, the shooter was confronted by police as he returned to an address that they were keeping under surveillance. Investigators described him as 25 to 30 years old with an athletic build and carrying a black automatic weapon. They released a blurred photograph of the suspect wearing dark clothes and a scarf covering part of his face.
Oliver Larsen, 26, who lives in a building above the street where the suspect was shot dead, said he was awoken at 5 a.m. by the sound of shooting.
"I looked out of the window to see what was going on and I saw a lot of policemen and a guy lying on the street; he was probably dead," Larsen told the AP.
Vilks, a 68-year-old artist who has faced numerous death threats for depicting Muhammad as a dog in 2007, told The AP he believed he was the intended target of the first shooting, which happened at a panel discussion titled "Art, blasphemy and freedom of expression."
"What other motive could there be? It's possible it was inspired by Charlie Hebdo," he said, referring to the Jan. 7 attack by Islamic extremists on the French newspaper that had angered Muslims by lampooning Muhammad.
The depiction of the prophet is deemed insulting to many followers of Islam. According to mainstream Islamic tradition, any physical depiction of the Prophet Muhammad — even a respectful one — is considered blasphemous.
While many Muslims have expressed disgust at the deadly assault on the Charlie Hebdo employees, many were also deeply offended by its cartoons lampooning Muhammad.
The attacks took place two days after Denmark and its partners in the European Union agreed to dramatically boost cooperation in the counter-terrorism field as a result of the January attacks in Paris, which claimed the lives of 17 victims.
The EU's law enforcement agency, Europol, said Sunday it was in contact with Danish authorities and proposing its help to find out as much as possible about the Copenhagen gunman and whether he was acting alone or in concert with others.
"We are offering our expertise and capabilities from our anti-terrorist unit including access to our databases," said Europol spokesman Soeren Pedersen.
Danica Kirka in London, Daniel Estrin in Jerusalem, John-Thor Dahlburg in Brussels and Kirsten Grieshaber in Berlin contributed to this story.
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