Merkel called for quotas to be set for each country to take a share of displaced people, many from war-torn Syria.
The crisis has to be solved in the spirit of European solidarity, Merkel said, speaking at a Berlin news conference with Swedish Prime Minister Stefan Lofven.
Sweden and Germany are taking on a high measure of responsibility, Merkel said, and a common European asylum policy has to be put into practice.
She also said the current international treaty setting out countries' responsibilities
for taking in refugees was no longer up to date, and that neither Greece nor Italy could take in all those crossing the Mediterranean Sea in search of sanctuary.
What is needed are quotas, which must be divided fairly, Merkel said. At the moment, Europe is far from that fair division, she added.
Some countries, particularly in Eastern Europe, are strongly opposed to any proposal for quotas, arguing they don't have the necessary resources.
Merkel's government has said Germany expects to receive some 800,000 asylum applications this year. The country could take 500,000 refugees
each year for "several years," Vice Chancellor Sigmar Gabriel has said.
Thousands of predominantly Syrian refugees have arrived in Germany over the past few days, passing through Hungary and Austria after making an overland journey north through the Balkans.
Authorities sometimes cannot control the migrants. On Tuesday, hundreds of frustrated migrants and refugees broke through police lines and ran from a holding area on the Hungarian-Serbian border.
The huge influx into Hungary prompted a crisis last week as Hungarian authorities sought to apply EU rules on registering newly arrived refugees in the first EU state they reach.
Faced by scenes of chaos as refugees couldn't travel onward from Hungary, Germany and Austria decided to relax the rules and let thousands of people in over the weekend without going through the usual process.
While that move eased the bottleneck in Budapest, the stream of migrants keeps coming.
A trash-strewn field along the Hungarian-Serbian border became a flashpoint
Monday as people grew weary of waiting for days in primitive conditions to resume their journey to safety.
On the same day, Austria and Germany warned they can't keep up with the influx of refugees and said they must begin to slow the pace.
More than 16,000 migrants have streamed into Austria since Saturday, Burgenland state police spokesman Wolfgang Bachkoenig said Monday. Virtually all continued to Germany, where the city of Munich had received more than 17,500 people, police said.
"We must now, step by step, go from emergency measures to a normality that is humane and complies with the law," Austrian Chancellor Werner Faymann said.
The U.N. refugee agency, UNHCR,
estimates that more than 366,000 refugees and migrants have crossed the Mediterranean to Europe this year.
About 20,000 are on the Greek island of Lesbos, spokeswoman Melissa Fleming said in Geneva. About 10,000 are on other Greek islands.
She said a record number -- 7,000 -- entered Macedonia, which shares a border with Greece, on Monday.
At least 2,800 have died or disappeared during the journey. Those who make the crossing face uncertain futures in European nations, which differ in their approach to asylum-seekers.
EU countries have an open-border policy that allows the free movement of people between member states.
While Germany, France and other countries are opening their doors to more migrants, countries such as Hungary are clamping down on the flow. Hungary's government has ordered the building of a barbed wire fence along its border with Serbia, a non-EU state.
U.N. Secretary-General Ban Ki-moon has talked with the leaders of Austria, Czech Republic, Germany, Greece, Hungary, Poland and Slovakia about the crisis.
Ban stressed the refugees and migrants have "a right to seek asylum without any form of discrimination," spokesman Stéphane Dujarric said.