About 200 people massed in the eastern town of Heidenau, some booing and shouting "traitor, traitor" and "we are the mob" as she arrived at the shelter, in a show of defiance over a record influx of asylum-seekers.
But following her visit, Merkel vowed: "There will be no tolerance of those who question the dignity of other people."
"The more people who make that clear... The stronger we will be and the better we will be able to address this task" of caring for refugees.
Police had sought to stop around 200 people trying to leave the country's main refugee processing centre there.
Budapest said it would send in police reinforcements to stem a record influx of asylum-seekers, as more than 2,500 people crossed into the EU country from its southern frontier with Serbia, days before a vast razor-wire barrier aimed at keeping out migrants is completed.
Europe is struggling to cope with its biggest migrant crisis since World War II -- from thousands of refugees landing on the shores of Italy and Greece to the hundreds climbing onto trucks to get from France to Britain.
Hungary is building a wall to keep migrants out, while the Czech Republic's deputy prime minister Andrej Babis called for the visa-free Schengen zone be closed with NATO deployment.
Germany, which is preparing to receive a record 800,000 asylum-seekers this year, instead eased the asylum application procedure for Syrians fleeing a brutal civil war.
Natasha Bertaud, spokeswoman for the EU Commission, said Berlin's move was "recognition of the fact that we cannot leave the member states at the external borders alone in dealing with a large number of asylum-seekers".
In practice, this means countries on the EU's southern borders like Greece or Italy are overwhelmed with applications.
But Berlin's largesse was not always welcomed at home, particularly in the east where a spate of attacks has hit refugee centres.
President Joachim Gauck blasted a "dark Germany" behind the series of xenophobic attacks, as German leaders went on the offensive to quell the wave of anti-migrant violence.
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