The Central Europeans have essentially refused to take migrants or refugees, rejecting the idea of quotas to help reception countries like Greece and Italy. The leaders of the four main countries of Central Europe — Poland, Hungary, the Czech Republic and Slovakia — have not even been invited to the Sunday meeting. And it was only with great trouble that Ms. Merkel convinced the new Italian prime minister, Giuseppe Conte, to come after he objected to an early draft of proposals made by the commission.

While the numbers of asylum seekers are way down, the long crisis still threatens one of the European Union’s greatest accomplishments, the “border-free” Schengen zone.

Countries have set up “emergency” border checks within the Schengen zone to block uncontrolled flow of migrants and possible terrorists, but those border controls are unlikely to be lifted. Mr. Seehofer’s desire to stop registered migrants from entering Germany would effectively mean setting up extensive new border controls with Austria, now run by a government in coalition with populists that also has decried uncontrolled migration.

But this is where anti-migrant policy, populism and nationalism create confused and sometimes contradictory positions. The border would antagonize both Austria and the new populist, anti-migrant government in Italy because it would stall migrants in Austria and mean sending back large numbers to Italy, where many migrants first registered. Having taken in some 650,000 boat migrants in the last five years, Rome objects to the idea of asylum seekers having to be returned to the country where they first registered.

Mrs. Merkel also fears that such a border would be copied by other countries within Schengen, effectively destroying it, perhaps forever. That is why she is trying to find a broader European solution, even if a temporary one.

But the tone is hardening generally toward migrants in Europe, with politicians of many stripes demanding better control over the bloc’s external borders, including as many as 10,000 more European border police. Yet no country seems eager to pay more into the European Union budget to cover the costs.

Hubert Védrine, a former French foreign minister and a Socialist, said recently that “populism is a measure of the failure of elites” to understand that “people want to retain an important level of identity, sovereignty and autonomy — and that means controlling migration.” Speaking at a meeting at the Château de Tocqueville, where Alexis de Tocqueville wrote “Democracy in America,” Mr. Védrine warned that if “migratory flows” are not controlled, “our democracy is at risk, and we will have populism or a form of European Trumpism, country by country.”

Ms. Merkel is also working on bilateral agreements with partners like Italy and Greece to reduce the burden on Germany, possibly similar to the deal struck with Turkey two years ago. She will also discuss the issue with Spain’s new prime minister, Pedro Sánchez, on Tuesday in Berlin. Spain displayed a kind of European solidarity when it agreed to accept the more than 600 migrants on a ship, the Aquarius, that the Italians turned away.