A man gunned down outside a Copenhagen synagogue early Sunday in one of three lethal shootings in the Danish capital was Jewish, a Jewish community group said on Sunday.

Michael Gelvan, chairman of the Nordic Jewish Security Council, told AFP that a bar mitzvah, or Jewish coming of age ceremony, had been underway inside the synagogue and that the "young man" had been responsible for "access control" when he was shot.

"We don't know anything yet, it's too early to guess," he said about possible motives behind the killing.

"But it's a copy of what happened in Paris," he said, referring to the deadly attacks at satirical weekly Charlie Hebdo and a Jewish supermarket in January.

In addition to the guard there were extra police outside the synagogue after community leaders contacted authorities following the afternoon gun attack on a debate about Islam and free speech at a community centre that left one dead and three police officers wounded.

The two police officers outside the synagogue were wounded but their injuries were not thought to be life threatening.

"I dare not think about what would have happened if (the killer) had access to the congregation," the chairman of The Jewish Community in Denmark, Dan Rosenberg Asmussen, told broadcaster TV2 News.