Italy's anti-migrant interior minister wants tighter criteria for granting humanitarian protection to migrants rescued at sea.
The EU is divided over the Dublin Regulation, under which the country where a migrant first arrives usually has to process his or her asylum claim.
He told reporters Thursday only "pregnant women, children and refugees" who are granted asylum among rescued migrants should remain in Italy.
Regarding a possible rejection of refugees to Hungary, Merkel explained that Germany has felt that Hungary seems to be not responsible for the Dublin rules, referring to the agreement reached in 2013 on the dealing with asylum seekers in EU.
Seehofer planned later on Thursday to hold talks in Vienna with Austrian Chancellor Sebastian Kurz, who has said his government would take measures to protect its southern borders - including with Italy where many migrants first set foot on European Union soil - if Germany proceeded with the transit zones.
But Mr Orban said the best way to be humane was to close borders and help the countries that migrants came from.
Interior Minister Horst Seehofer, who had proposed turning back those asylum seekers at the border, a move that threatened to collapse the government, said he was very pleased by the agreement.
Migration will also be prominent during talks in Berlin later on Thursday between Merkel and anti-immigrant Hungarian Prime Minister Viktor Orban, who has said he is ready to strike a bilateral deal with Germany to limit the migrant arrivals.
At a joint news conference in Berlin, she said if Europe wanted to retain its soul it could not ignore people's needs and suffering. The party blocked a similar proposal for migrant processing centres on the border in 2015.
Mrs May said she is hopeful the meeting will increase the "pace and intensity" of Brexit negotiations between the United Kingdom and EU.
"With this, the entire coalition has committed to the goal to order, control and limit migration", she said. That compares to a total of 164 Turkish nationals who sought asylum in Norway in 2017. They said there are over 300 German automotive facilities in the United States, supporting almost 120,000 jobs.
In 2017, a total of 15,414 people applied for asylum at German borders, with 1,740 of those applications made at the German-Austrian border - or around 4.7 per day, according to data from Seehofer's ministry provided to Left party lawmakers.
On Wednesday Mrs Merkel agreed to tighten controls at the Austrian border to stop people who have applied for asylum in other European Union countries from entering Germany.
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