A string of attacks on women in Cologne on New Year's Eve blamed largely on foreigners was "intolerable", German Chancellor Angela Merkel's spokesman said, but "nothing excuses" retaliatory assaults on immigrants.
Mrs Merkel has proposed making it easier to deport immigrants involved in crimes, and her spokesman Steffen Seibert emphasised the government is looking into both "possible consequences for criminal law (and) possible political consequences for the intolerable crimes".
But after Cologne police said a group of Pakistanis and a Syrian were attacked in the city on Sunday, Mr Seibert said Germans must not blame all the nearly 1.1 million migrants who entered the country last year, and said the government is also focused on their welfare.
"We're doing all of these things to protect the population in Germany," he said. "We are also doing this for the great majority of innocent refugees who have sought refuge from bombs and war in our country, and who should get this protection and who are prepared to adapt to the rules and values in our country."
The six Pakistani nationals were attacked on Sunday by around 20 people and two of them were briefly admitted to a hospital, police said. Also on Sunday evening, a Syrian man was attacked by five people. He was injured but did not need treatment.
Police said they received tips on Sunday afternoon about groups of people who would "seek provocation", but were still investigating whether the subsequent attacks were racially motivated and whether there was any link to the New Year's assaults.
Those assaults stoked tensions over Germany's open-door policy to refugees and prompted politicians to call for tougher laws against migrants who commit crimes.
"As abominable as the crimes in Cologne and other cities were, one thing remains clear: there is no justification for blanket agitation against foreigners," justice minister Heiko Maas said, adding that some people "appear just to have been waiting for the events of Cologne".
Authorities and witnesses said the New Year's Eve attackers were among a group of about a thousand people, described as predominantly Arab and North African men, who gathered at Cologne's central train station. Some broke off into small groups and groped and robbed women, police said.
Mr Maas has said German authorities need to quickly determine whether the assaults were coordinated, and may have been linked to similar offences in other cities including Hamburg. Incidents were also reported in Sweden and Finland.
North Rhine-Westphalia state police told politicians, however, that so far their investigation had found no indication the Cologne attacks were coordinated, or linked to others, the dpa news agency reported.
Cologne police say 516 criminal complaints have now been filed with them in connection to the New Year's attacks. About 40% involve allegations of sexual offences.
Cologne's police drew criticism both for its response and for its slowness to release information. Police chief Wolfgang Albers was dismissed on Friday by North Rhine-Westphalia state's interior minister, Ralf Jaeger.
At a session of the state legislature's home affairs committee, Mr Jaeger said Cologne police had not called in reinforcements who were offered.
Mr Jaeger said that witness and police reports "indicate that it was almost exclusively people with an immigrant background who committed these crimes".
Of the 19 suspects identified by name by Cologne police, 10 were asylum-seekers and the other nine were believed to be in Germany illegally, according to a report Mr Jaeger submitted to the committee.
None were registered as living in Cologne, and four are now in custody for robberies committed during the New Year events.