BERLIN (Reuters, AFP) - Chancellor Angela Merkel promised on Thursday to protect Jews and Muslims living in Germany from prejudice, saying vibrant democracy was the best way to combat the sort of extremist violence that shook France last week.

Merkel, a staunch ally of Israel and defender of Germany's renascent Jewish community, has responded with unusual vigour to the growth of a grassroots, anti-Islam movement in Germany and the attacks by Islamic radicals in Paris that killed 17 people.

Saying that Islamist extremism and anti-Semitism "often go hand-in-hand", she told the Bundestag lower house of parliament that Christians, Jews and Muslims all had a place in Germany. Echoing her comments on Monday that "Islam belongs to Germany", she said: "Jewish life belongs with us."

"We will prosecute anti-Semitic crimes by all legal means,"she said during a debate on the Paris attacks. "And attacks on mosques will be prosecuted rigorously, because we won't be divided by those using Islamist terrorism to cast suspicion on all Muslims in Germany.

"As chancellor I will protect Muslims in our country. All of us in this house will do that," she said.

Merkel is criticised by some of her own Christian Democrats for her impassioned defence of Germany's 4 million Muslims. They accuse her of playing down Germany's Judeo-Christian roots. The debate has been inflamed by the growth of PEGIDA, or Patriotic Europeans Against the Islamisation of the West, whose weekly marches in Dresden call for stricter immigration rules.

Some members of a new right-wing party, Alternative for Germany, have allied with PEGIDA in chiding Merkel for letting the number of asylum seekers shoot up 60 percent last year.

Police in Dresden were investigating the stabbing death of a 20-year-old asylum-seeker from Eritrea, local media reported, amid speculation it might be a hate crime.

A poll conducted before the Paris attacks said 57 percent of non-Muslims in Germany felt threatened by Islam. But Merkel said law-abiding Muslims needed protection from "hate preachers" and groups such as Islamic State in Iraq and Syria (ISIS) who were trying to radicalise them.

After moving to tighten a travel ban for suspected extremists, her cabinet would soon stiffen penalties for financing terrorism, she said. Germany would also keep providing weapons and military training to Kurdish troops fighting ISIS.

The government also wants to facilitate the use of data from phone calls and airline passenger lists to fight extremism.

Merkel stressed the need for online surveillance and for intelligence cooperation with foreign services - controversial topics in Germany following the revelations by former US intelligence contractor Edward Snowden about the NSA's mass snooping activities.

While she said there must be a "balance between freedom and security", she stressed that "there is also no doubt that the exchange of information across national borders is absolutely essential for our security".

At the EU level, she urged progress on plans to combat the illegal arms trade, to better monitor the bloc's outside borders and to exchange air passenger data.

Merkel also urged the European Commission to move forward with a new directive to compel telecoms to retain all phone, email and Internet communication data for certain periods, after similar initiatives were struck down by German and European courts.

She said there was now broad consensus among German interior ministers at the federal and state levels that "we need minimum data retention periods", which she hoped to soon see adopted in German law.

But Merkel said the best defence was to "shake up society's democratic principles", calling this "stronger than terrorism".

Recalling that 66 reporters were killed around the world in 2014, as well as 12 at the French satirical weekly Charlie Hebdo last week, Merkel said freedom of the press was essential for democracy but in too many countries it existed only "on paper".

Bundestag President Norbert Lammert criticised Saudi Arabia for condemning the Paris attacks as a violation of Islam, "then two days later letting the blogger Raif Badawi be flogged in public in Jeddah for insulting Islam".