Former Danish Chief Rabbi Bent Lexner (L) and President of the Jewish Society in Denmark Dan Rosenberg Asmussen give a news conference in Copenhagen February 15, 2015. Danish police have identified the gunman believed responsible for two deadly shootings in Copenhagen and believe he may have been inspired by last month's Islamist militant attack on French satirical weekly Charlie Hebdo, a spokesman said on Sunday. REUTERS/Claus Bech/Scanpix (DENMARK - Tags: RELIGION CRIME LAW) ATTENTION EDITORS - THIS IMAGE HAS BEEN SUPPLIED BY A THIRD PARTY. IT IS DISTRIBUTED, EXACTLY AS RECEIVED BY REUTERS, AS A SERVICE TO CLIENTS. DENMARK OUT. NO COMMERCIAL OR EDITORIAL SALES IN DENMARK

By Alexander Tange and Ole Mikkelsen

COPENHAGEN (Reuters) - Denmark's small but vibrant Jewish community rebuffed Israel's call to emigrate on Sunday after an attack on Copenhagen's main synagogue that shook the sense of security Scandinavian tolerance had long provided.

Jewish communities around Europe have been reporting rising hostility against them and an attack last month on a Paris kosher supermarket killed four Jews, prompting the United Nations to say that anti-Semitism was thriving in Europe.

That assault came two days after Islamist militants gunned down 12 people at the weekly Charlie Hebdo, which had published cartoons mocking the Prophet Mohammad.

As in the French case, Israeli Prime Minister Benjamin Netanyahu told Denmark's 2,500 Jews they would be welcome in his country. "Israel is your home," he said in Jerusalem.

"We appreciate the invitation, but we are Danish citizens, this is our country," Dan Rosenberg Asmussen, chairman of the Jewish Society in Denmark, told Reuters as he offered condolences to mourners at the synagogue.

The Copenhagen shootings began with an assault on a meeting with an artist who had caricatured Mohammad, and then an attack on the city's main synagogue where about 80 Jews celebrated a girl's confirmation. One person was killed at each site.

Danish police have not identified the gunman, who was killed in a shootout on Sunday, but said the attacks may have been inspired by the violence in Paris.

“I feel just as safe on the streets today as I did the day before yesterday," said Jewish community member Bent Bograd as he laid flowers at the synagogue. "We can’t do anything about it, and it’s a risk that exists.”

Denmark has welcomed Jews for centuries and most of the community survived the Holocaust, despite Nazi occupation, as Danes helped them flee to safety in neighbouring Sweden.

Only a fraction of the community returned but it enjoyed a long period of tranquillity. But tensions rose last year during Israel's war with Hamas militants in Gaza. Copenhagen's 210-year-old Jewish school was vandalised in August when its windows were broken and walls covered with anti-Semitic graffiti.

Yair Melchior, Copenhagen's chief rabbi, flatly rejected the idea that Jews should leave Denmark.

"The terrorists must not control our lives," Melchior told Reuters. "We need to concentrate on living our lives as normally as possible after this difficult situation. The Jewish community in Copenhagen is strong."

(Writing by Balazs Koranyi; Editing by Tom Heneghan)