Germany has announced plans to make it easier to throw out foreign criminals and remove refugee status if for those who had committed sex attacks.
The decision follows hundreds of sexual assaults and robberies on women in Cologne on New Year's Eve by men of mainly Arab and North African origin.
Justice Minister Heiko Maas said no-one could put themselves above the law.
Thousands of far-right protesters on Monday blamed the Cologne attacks on Germany's influx of refugees.
More than 1.1 million people claimed asylum in Germany in 2015.
Police in Cologne say 553 criminal complaints have been filed by women in Cologne, almost half for sexual assault.
The authorities said on Monday the perpetrators were almost exclusively from an immigrant background.
Speaking days after Chancellor Angela Merkel said "clear signals" had to be sent to potential offenders, Mr Maas said on Twitter that the core of the government's reforms would be to ease extradition of foreign criminals and strip them of refugee status if they had committed particular offences.
Penalties for sexual offences would be appropriate "regardless of current events", a government statement said.
"We will tighten criminal law to make deportation easier," Mr Maas said, adding that binding agreements would be sought with offenders' country of origin.
But he stressed that migrants should not come under general suspicion.
Several women in Cologne were raped and the justice minister said the definition of the offence in German law was too narrow. "There's no clear answer in law to how much resistance a woman has to offer for an offence to constitute rape," he said.
Some 2,000 supporters of Legida, the Leipzig version of the Patriotic Europeans Against the Islamisation of the West movement (Pegida), marched through the city on Monday.
They vented their anger at Chancellor Angela Merkel over her government's open-door policy on refugees.
As the protest took place, a group of far right extremists and football hooligans went on the rampage in the largely left-wing district of Connewitz, police said. Officers made 211 arrests as buildings were vandalised and vehicles burned.
Protesters opposing Pegida also held a counter-demonstration in Leipzig on Monday evening.
Left-wing activists vandalised a bus that had been hired by the far-right supporters. The police statement did not say whether any leftists had been detained.