Danish police said that a gunmen shot dead by officers after deadly attacks on a cultural centre hosting a freedom of speech event and a synagogue, may have been inspired by the attack on French satirical magazine Charlie Hebdo last month.

The gunman, who has not been named, was known to police, officers said.

He "may have been inspired by the events that took place in Paris a few weeks ago", Jens Madsen from the Danish Security and Intelligence Service told reporters, reports AFP.

He said the man may "generally have been inspired by militant Islamist propaganda issued by IS [ISIS] and other terror organisations".

Officers are investigating whether the man travelled to Syria or Iraq, where radical Sunni organisation ISIS hold stretches of territory.

The man is believed to be responsible for an attack on an event on freedom of speech, attended by the French ambassador and the Swedish cartoonist Lars Vilks, in which a 55-year-old man was killed, and a subsequent attack on a synagogue in the early hours of Sunday morning, in which a 37-year-old Jewish security guard was killed.

Five police officers were wounded in the attacks.

The gunman was killed by police when returning to an address in Copenhagen which was under police surveillance.