But Bavarian interior Minister Joachim Herrmann said on Sunday that the federal government had rejected the request from Munich.
"I can't understand at all," Herrmann told the Welt am Sonntag newspaper. "That we are not carrying out reliable controls, even five weeks after the Paris attacks and despite the blatant danger, is a sign of weakness."
A spokeswoman for the Federal Ministry of the Interior pointed out that the federal government alone has jurisdiction over Germany's national borders.
The calls for improved border security from Bavaria's governing Christian Social Union (CSU) were added to grumbles from their allies in Chancellor Angela Merkel's Christian Democratic Union (CDU).
"Our state must know who is on our territory," said CDU deputy leader Julia Klöckner.
"We can't behave as if saints were coming into our country when people are falsifying passports."
Foreign Minister Frank-Walter Steinmeier said that the only solution was better controls on the European Union's external borders.
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The EU must "have more control over who is travelling into and out of Europe," Steinmeier told the Funke newspaper group on Sunday.
But he warned against those who wanted to "mix up refugees with alleged terrorists" – noting that the vast majority of Muslim fundamentalist attackers have so far come from within Europe.