“What we are experiencing now is something that will occupy and change our country in coming years,” she said after 20,000 migrants arrived at the weekend alone.
“We want the change to be positive, and we believe we can accomplish that,” she added.
Merkel said scenes of spontaneous solidarity from hundreds of Germans who greeted families fleeing wars in Syria and beyond at railway stations with gifts and welcome signs were “very moving” and “breathtaking”.
“That is something very valuable, especially in view of our history,” she said, expressing joy that “Germany has become a country that many people abroad associate with hope”.
She stressed that other EU countries must take in more migrants because “only with common European solidarity can we master this effort”.
Merkel called for a “solidarity-based and fair distribution of refugees” and said the “Europe based on values must show its face”.
Germany — which expects 800,000 asylum requests this year, four times last year’s total — said her country could face costs of 10 billion euros ($11 billion) next year.
“That order of magnitude doesn’t seem implausible to me,” she said at a joint press conference with centre-left Vice Chancellor Sigmar Gabriel.
Their ruling coalition pledged an additional six billion euros in federal funds for 2016 and said the rest of the money would come from states and communes.