Orban said that his country built a fence on its southern borders to regain control over its territory, the move protecting not only Hungary but also Germany by not allowing refugees to enter Hungary.
Now the numbers of such migrants arriving at Bavaria's border with Austria are 10 or fewer daily, the German government says.
Last week, Merkel had ensured that up to 14 European Union countries had pledged to accelerate return of registered asylum seekers in or countries arriving in Germany, including Hungary, which immediately denied having reached an agreement with Berlin about it.
German Federal Interior Minister Horst Seehofer said after the meeting that there would be no transit centers, as agreed by the Merkel-led Christian Democratic Union (CDU) and Seehofer-led Christian Social Union (CSU) on Monday.
Seehofer sought to allay concerns from Nahles' party of large migrant camps on the borders, assuring that the so-called transfer centers he wants to establish "would have no barbed wire or the like", and would be set up in existing police stations that would deal with the cases of only a handful of migrants a day.
"We agreed. that next week there will be a meeting of the German, Austrian and Italian interior ministers with the goal of taking measures to shut the Mediterranean route into Europe, to make sure that illegal immigration to Europe on this route is stopped", Kurz told a joint news conference.
Referring to the country's current defence budget of 38.9 billion euros, Merkel said, "Measured against what other countries do in relation to their GDP, it is not remotely enough".
"We think it's unfair that Germany often accuses us of a lack of solidarity", Orban said. "I am confident that we will reach an agreement with the SPD as well", he said.
"We have reached an agreement after an intensive debate".
Fifty-six percent of Germans felt too much focus was being put on migration, to the detriment of other issues.
Migrant arrivals peaked in 2015 at more than a million people, many of them fleeing the Syrian war and therefore entitled to asylum, while others were trying to escape poverty.
Some in the SPD have accused Seehofer of sparking the coalition crisis for purely self-serving reasons - his CSU fears hemorrhaging voters to the anti-immigrant Alternative for Germany in Bavaria's state election in October.
German Interior Minister Horst Seehofer on Thursday went to Vienna to discuss a possible agreement that Austria would be willing to accept certain refugees from the planned transit centres.