"We need to take emergency measures to stem the flow of refugees, for example turning them back at the Austrian border or sending asylum seekers immediately on into other German states," Bavaria's minister president Horst Seehofer told the Bild newspaper.
Seehofer did not go into details of how such a policy would work. The Austrian border is controlled by the Federal Police, which comes under the control of the federal government in Berlin, not the Bavarian government in Munich.
Austria reacted with immediate anger to Seehofer's comments. "If Bavaria starts to slow down the flow of refugees and to put more controls in place, then Austria will be forced to take similar measures," Austrian Interior Minister Johanna Mikl-Leitner said.
She added that if refugees were sent back Austria would have a “humanitarian crisis” on its hands - and that there could be violent protests and riots if people who want to stay in Germany are forced to return to Austria.
Bavaria for its part has expressed anger that Austria allows refugees to travel unopposed into the southern German state, meaning thousands arrive daily.
The German human rights organisation Pro Asyl has criticised Seehofer's threats to send refugees back to Austria - saying such a move would be illegal and refugees can only be sent back to whichever EU state is originally responsible for them.
The Bavarian leader's comments are also likely to bring him into further conflict with Chancellor Angela Merkel.
The two leaders of Germany's "Union" of conservative parties have repeatedly expressed opposing views on the refugee crisis in recent weeks.