Separately, Merkel said she wanted to protect Europe's "humanity" in dealing with migrants, spelling out her differences with Hungary's prime minister, Viktor Orbán, at a press conference in Berlin.
Speaking at a joint news conference after their meeting in Berlin, Merkel said despite recent moves by European Union nations to clamp down on asylum-seekers moving across Europe's open borders, she wants to ensure they are treated with "humanity" and the continent isn't turned into a "fortress" Europe.
Merkel said that securing the external borders of the European Union is not the creation of a "fortress against the people, brought by the smugglers".
The two-page agreement, reached after a short meeting at the historic Reichstag building, ends a bruising dispute that had threatened to tear apart Chancellor Angela Merkel's "grand coalition" just months after it took power, and left the four-term leader politically weakened.
"Germany and Hungary see the world differently", said Orban, one of the strongest critics of Merkel's migration policy since 2015, when thousands poured into Europe every day.
Mr Orban said it was essential to remove pull factors that he said were encouraging people in Africa and Asia to migrate.
Austria has become an enthusiastic supporter of a long-standing effort by the European commission to create a European border and coastguard agency, in contrast to the policy of previous Austrian governments.More news: Stop Mbappe! Uruguay's tactic v France for quarter-final
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Frode Forfang, head of Norway's Directorate of Immigration, says many have claimed political persecution at home because of links to US -based Muslim cleric Fethullah Gulen, who is blamed by Turkey for the 2016 failed coup.
Italy's anti-migrant interior minister wants tighter criteria for granting humanitarian protection to migrants rescued at sea.
Ms Merkel would have hoped she had put the crisis that threatened to bring down her government behind her when she hammered out the last-minute compromise with Horst Seehofer, her rebellious interior minister, on Monday night.
But this is also causing some disagreement.
The announcement comes after hard negotiations between Chancellor and his Interior minister, Horst Seehofer, who agreed to establish closed migrant centres on German-Austrian border to accelerate return of asylum seekers To first community country where y were registered.
"We think that the people Germany is sending back must go to Greece and not Hungary. Instead we drafted a new proposal that includes reasonable solutions, and the CDU/CSU has performed a piece of theater in the last three weeks that was unworthy of this country, our country", Nahles said. However, Italy - the main arrival point for most migrants from North Africa - does not yet have a bilateral deal with Germany.
The agency said that 245 Turkish nationals have sought shelter in Norway so far in 2018, including 142 arriving in June.