“If the requirements of the EU’s Schengen and Dublin agreements can not be promptly implemented again then the Federal Republic of Germany should send refugees back from the border“.

Over 200,000 migrants are estimated to have entered Germany since the beginning of September, the vast majority over the Austrian border into Bavaria.

The entire programme is to cost about €489m (£363m), he said, adding that while it seemed like a lot of money, “it will be money well spent, because the costs to us if integration fails will be a lot higher”.

Meanwhile, a right-wing party said it plans to lodge a legal complaint against Ms Merkel, accusing her of “people smuggling” for letting thousands of migrants into the country after they got stuck on the Hungarian border.

“One [the German government] does not comply with the law and the other [Bavaria] wants the law to be complied with,” Bavarian Prime Minister Horst Seehofer said, commenting on the decision at the press conference following the meeting.

After the meeting, the Bavarian interior minister Joachim Herrmann threatened to take the government to court if it did not limit the flow of asylum seekers.

Bavaria’s conservative Christian Social Union government has criticized Merkel’s policy, introduced last month, of registering refugees in Germany rather than expelling them.

He also warned against what he called a “clandestine acceptance” among society.

The anti-immigration party claimed it would file a lawsuit with the Berlin public prosecutor’s office requesting that it open preliminary proceedings against the chancellor.

EU’s largest economy Germany accepts more refugees than any other European Union member. According to German Interior Minister Thomas de Maizière, two-thirds of the attacks were carried out by people who had no prior criminal record.

“Merkel’s toughest battle”, ran a headline in Bild, Germany’s top-selling newspaper, which judged that “the refugee crisis is decisive for the political future of the chancellor”.

Diplomatic sources said Merkel’s officials in Berlin have been testing out hypothetical scenarios of reforms that the British may seek, since there has been no clear signal from London of what they might entail. More are continuing to arrive at a rate of about 1,000 a day.