In their meeting, Mr. Kerry and Mr. Steinmeier also focused on ways to end the war in Syria, where 250,000 people have died and 12 million have fled their homes in the past four and a half years. In addition, Germany and the United States will try to rally support next week at the United Nations General Assembly for a significant increase in aid to United Nations refugee camps in the countries neighboring Syria, Mr. Steinmeier said.

The American response is unlikely to relieve much of the pressure on European countries, particularly Germany, which remains the most desirable destination for most of the migrants. Other efforts to address the crisis, such as agreeing to distribute migrants equitably among European Union members, have foundered so far, and in the absence of a unified and effective policy, the migrants have been left to find their own way across the Continent.

Germany recently has been under pressure from a seemingly unstoppable influx of migrants, and it reinstated border checks a week ago to better manage the crowds. The flow from Austria slowed over the weekend to less than 2,000 registered arrivals each day, according to Lars Rebel, a spokesman for the German federal police.

But Austria received about 20,000 newcomers over the weekend on its eastern border with Hungary. Most “still want to go to Germany, their great goal, their great dream, their great vision,” said Alexander Marakovits, a spokesman for Austria’s Interior Ministry in Vienna.

At least 10,000 arrived or passed through Sunday at the small Austrian village of Nickelsdorf, a city in the state of Burgenland near the border with Hungary that links Budapest to the east and Vienna to the west, Mr. Marakovits said.

The main highway linking the two cities was closed amid concerns that crowds of refugees would spill into traffic. Although everyone insisted the flow was manageable, the director of the state’s police, Hans Peter Doskozil, hinted at the strain.