"The focus will initially lie on the border with Austria," de Maiziere said. "The goal of this measure is to restrict the present inflow of migrants into Germany and return again to an orderly process upon entry."

Germany is stopping train traffic to and from Austria for 13 hours, the Austrian Federal Railways said in a tweet. The moratorium on train travel between the two countries will last from 5 p.m. Sunday (noon ET Sunday) until 6 a.m. Monday, the railway agency said.

The announcement of measures by Germany came hours after more than 40 migrants were discovered alive inside a refrigerated truck in northwest Austria, about 50 kilometers (30 miles) from the German border.

The rescue of those migrants may have prevented a deadly fate if something had gone awry on their covert trip, but others were not so lucky.

Nearly 30 people -- almost half of them children -- were found dead off the coast of the Greek island of Farmakonisi on Sunday, the Hellenic coast guard said.

At least 125 people were aboard a wooden boat that capsized in the Aegean Sea, coast guard duty officer George Tsapras said. The coast guard rescued 68 people, 29 others swam to shore, and another 28 died.

Search and rescue efforts were ongoing, Tsapras said.

It is unclear if those on the boat were refugees or migrants, as their nationalities and points of origin have not yet been identified, Tsapras said.

Europe struggles for a solution

European leaders have been struggling to cope with the massive influx of people pouring across its borders in recent weeks.

Last week, European Commission President Jean-Claude Juncker set out proposals for mandatory quotas for EU countries to take in 120,000 refugees who were already in Italy, Greece and Hungary, on top of plans made in May to relocate 40,000 from Italy and Greece.

EU member states must still agree to the European Commission's proposals, which are backed by Germany. Their interior ministers are due to meet Monday in Brussels, Belgium, to discuss the issue.

As many as 10,000 migrants are arriving in Germany per day, according to German Interior Ministry spokesman Tobias Plate. Officials throughout the country have been asked to assist with registration and accommodation needs, he said Saturday.

The German interior minister said the border controls are for "security reasons urgently necessary."

Rescued from a flower truck

A total of 42 people were inside the refrigerated truck found in Austria, police spokesman Bernd Innerdorfer said.

Police discovered the truck, belonging to a Finnish flower transporter, at a gas station in the city of Aistersheim. It was being driven by two Iraqi nationals, who were arrested and charged with human smuggling.

Five women and eight children were among those rescued. All of them were in good health, did not require any medical attention and were transported to a refugee detention center in the city of Linz, Innerdorfer said.

The migrants are believed to be Syrian and Iraqi, police said, but their identities were not immediately confirmed.

Full coverage: The migration crisis

CNN's Mariano Castillo contributed to this report.