Updated at 3:10 p.m. ET
Germany's interior minister confirmed Sunday that his country would impose temporary controls on its border, halting trains between Austria and Germany for a 12-hour period to stem the flow of refugees flooding into Munich.
"The aim of these measures is to limit the current inflows to Germany and to return to orderly procedures when people enter the country," Thomas de Maiziere said at a news conference.
He said refugees could "not choose" their host countries and he urged the European Union to take steps to resolve the crisis.
Bild newspaper and Austria's Kronen Zeitung had earlier reported that the controls were pending after more than 12,000 migrants arrived over a 24-hour this weekend.
The announcement came as officials in Munich warned they had reached "the upper limit" of what the Bavarian city could take. Authorities predicted that 40,000 refugees would come in just a few days, adding to the hundreds of thousands in total that were expected this year.
"We have reached the upper limit of our capacity," federal police spokesman Simon Hegewald.
Munich has been the entry point for the mainly Syrian refugees who have sought to escape war and economic distress. Migrants from places such as Afghanistan and Eritrea in east Africa are also on the move. Munich is stretched to the limit to accommodate and house them, according to the mayor.
"We no longer know what to do with refugees," Dieter Reiter was quoted by Agence France-Presse as saying.
As the BBC reports: "More than 4,000 people walked across the border with Serbia - the most so far in one day - just as the authorities in Hungary were completing preparations to seal the frontier."
Demonstrations for and against the migrants have been staged in several European cities. In some, people carried signs reading "Refugee lives matter" and other placards simply stated "go home."
As NPR's Lauren Frayer reports from Budapest, new laws in Hungary take effect on Tuesday "that will make it illegal for anyone to cross Hungary's borders without a visa — even asylum seekers."
As The Associated Press notes "many ... fear that Muslim arrivals will threaten their jobs and security."
On Monday, European Union is scheduled to meet in Brussels to discuss ways to handle the sudden influx of migrants. The EU is said to be considering a quota system that would have member states agreeing to take in and settle a specific number of them.
Meanwhile, Pope Francis has renewed a call urging Catholics to open parishes to shelter refugees.
Last week, Austria experienced an influx of migrants, most coming from Hungary en route to Germany. But Hungary shut down the train link on Thursday.
"Only 50 people crossed the [Austrian] border early on Sunday morning, but Hungarian authorities had said more were on their way and numbers could climb to 500 an hour, a spokesman for the Austrian police said.
"Based on recent experience, the Austrian authorities were expecting 6,000-8,000 new arrivals through the day, the spokesman added."