German Chancellor Angela Merkel remains firmly opposed to unilateral moves to turn some refugees back at the border - as demanded by conservative allies in her own government, warning such action would weaken the European Union.
Tempers within the government have frayed over the issue in recent days and the dispute has raised questions over Merkel's future, as nationalist forces already in power elsewhere in Europe turn up the heat on the long-serving chancellor for her welcoming stance toward migrants.
Among Merkel's sharpest critics is Bavarian governor Markus Soeder, whose Christian Social Union is taking an increasingly hard line ahead of a state election this fall, even though it forms part of the governing coalition at the national level.
Soeder and his party's leader, Horst Seehofer - Germany's interior minister - want to send police to the southern border to turn back migrants who have registered as asylum-seekers in other European countries.
Merkel has warned that such a move could shift the burden onto countries such as Italy and Greece that have struggled to cope with the influx of migrants coming across the Mediterranean.
"We must not contribute to weakening the European Union and purely national measures setting the tone again in Europe," Merkel's spokesman, Steffen Seibert told reporters in Berlin.
In a sign of how jittery the German establishment has become, a hoax tweet suggesting Seehofer had broken up his party's decades-old alliance with Merkel's conservatives was picked up widely by German media, briefly sending the euro currency into a nosedive against the US dollar.
Other members of Merkel's government turned to name-calling, with Andrea Nahles, the leader of Germany's center-left Social Democrats, accusing Soeder of "behaving like a bonsai Trump."
Nahles said her party, which is also a member of the governing coalition in Berlin, backs Merkel's call for a Europe-wide consensus on how to tackle the issue of irregular migration.
Commentators in Germany have noted that the spat is one of the biggest crises for Merkel, who was recently elected for a fourth term with only a narrow majority. However it ends, this week's crisis has underlined that there are limits to her power.
The German government has already imposed numerous measures to reduce the influx of refugees since 2015, when the number of migrants coming to Germany peaked follow Merkel's decision not to close the border to people coming through Hungary and Austria.
The country of some 80 million now sees about 11,000 new asylum-seekers per month. Of these, some 30 per cent could end up being turned back at the border if current European Union rules on asylum are applied, according to German officials.