A man who opened fire on police and who might have been involved in two attacks that took place in Copenhagen has been killed, authorities say.

Police have reported he was shot dead in the district of Nerrebro, an area of Copenhagen which has a vast immigrant population.

On Saturday and the small hours of Sunday, two people died and a few others were wounded after a man opened fire at two locations in the Danish capital.

The second attack, which occurred near a synagogue, claimed the life of a Jewish man and left two officers wounded. The victim was a young man who had been in charge of security at the moment. There had been about eighty people at the synagogue on Saturday night to take part in Bar Mitzvah rituals.

The first took place on Sunday afternoon at a cafe where an event dedicated to freedom of speech was to take place. It had been organized by a man famous for his cartoons depicting Prophet Muhammad as a dog. 

Francois Zimeray, the French ambassador to Denmark, was also attending the Saturday event.

Police have not fully confirmed, but believe the two attacks were interlinked and the man shot by police was involved.

Danish authorities say they consider the two incidents to be "terror attacks."

The US has already offered to help Denmark investigate into the two attacks.