Growing scale of Cologne attacks stokes German debate on migrants
Almost three quarters of those polled said migration was the most important issue for the government to deal with in 2016.
The Cologne attacks also heated up the debate on immigration in neighboring Austria.
"What happened in Cologne is unbelievable and unacceptable," Austrian Interior Minister Johanna Mikl-Leitner, a member of the conservative People's Party that is junior coalition partner to the Social Democrats, told newspaper Oesterreich.
There had been a handful of similar incidents in the border city of Salzburg. "Such offenders should be deported," she said, backing a similar suggestion by Merkel.
Swiss media contained numerous stories about sexual assaults on women by foreigners, fuelling tensions ahead of a referendum next month that would trigger the automatic deportation of foreigners convicted of some crimes.
In Germany, on Monday, a regional parliamentary commission will quiz police and others about the events on New Year's Eve in Cologne.
The anti-Islam PEGIDA, whose supporters threw bottles and fire crackers at a march in Cologne on Saturday before being dispersed by riot police, will later hold a rally in the eastern German city of Leipzig.
The far-right will likely seize on reports that the Paris attacker, who was shot last week as he wielded a meat cleaver and shouted "Allahu akbar" (God is Greatest), was known to police for drug dealing and harassing women.
He had an apartment in an accommodation center for asylum seekers in Recklinghausen, north of Cologne, where he had painted the symbol of Islamic state on the wall of two rooms.