Germany has seen a sharp rise in attacks on asylum centres, as it deals with record numbers of arrivals.
Earlier, police in Hungary used tear gas to disperse migrants protesting at a reception camp on the Serbian border.
Unrest flared at a crowded centre at Roszke. Hungary has said it is considering the use of troops to secure the border.
Germany expects up to 800,000 asylum applications in 2015 - more than any other EU country.
The chancellor has condemned as "repulsive" the weekend`s far-right protests in the eastern town of Heidenau, near Dresden.
Neo-Nazis and other right-wing extremists hurled bottles and fireworks during the demonstrations, injuring dozens of police officers.
Mrs Merkel faced activists who shouted "traitor" as she visited the centre in Heidenau on Wednesday. Protesters do not want the former DIY store to be used as an asylum shelter.
They chanted "for the German people" - referring to the sign on the front of the Reichstag - and "We are the mob", repeating the term used by Vice Chancellor Sigmar Gabriel to describe far-right and racist activists in the town.
Motorists also reportedly hooted their car horns as they drove past - something that right-wing groups had called for on social media.
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