"Universal civil rights have been closely linked with Europe and its history as a founding impetus of the European Union," she said.
"If Europe fails on the question of refugees, if this close link with universal civil rights is broken, then it won't be the Europe we wished for," she said, urging other EU members to accept their fair share of asylum seekers.
Speaking to foreign journalists in Berlin, Merkel said: "Europe as a whole needs to move. Member states must share responsibility for asylum-seeking refugees."
"If we don't arrive at a fair distribution then the issue of Schengen will arise -- we do not want that," she said, referring to the visa-free zone covering much of the EU and several neighbouring countries.
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Merkel expressed confidence that Europe would rise to the challenge, pointing to previous issues it had mastered, such as the 2008 banking crisis, and to problems Germany itself has overcome, from the 1990 reunification to its ongoing nuclear phase-out.
Merkel said Germany must cut red tape to quickly build more shelters and train more language teachers, saying that while German "thoroughness is super... What we need now is German flexibility".
Italy especially must be offered help from other EU nations as it had taken in huge numbers of migrants arriving via the Mediterranean Sea, the chancellor said.
She implicitly criticised countries including Slovakia that have rejected migrants from Islamic countries, saying: "if we start saying 'I do not want Muslims' ... That cannot be good".
"There will be zero tolerance for those who put in question the dignity of other people," she said.