(CNN) The flood of migrants pouring into Europe means all European Union member states must step up to meet the mounting crisis, German Chancellor Angela Merkel said Tuesday.

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.

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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.

Border flashpoint

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.

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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.

Uncertain futures

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.

Photos: Europe's migration crisis in 25 photos Photos: Europe's migration crisis in 25 photos A woman cries after being rescued in the Mediterranean Sea about 15 miles north of Sabratha, Libya, on July 25, 2017. More than 6,600 migrants and refugees entered Europe by sea in January 2018, according to the UN migration agency , and more than 240 people died on the Mediterranean Sea during that month. Hide Caption 1 of 26 Photos: Europe's migration crisis in 25 photos Refugees and migrants get off a fishing boat at the Greek island of Lesbos after crossing the Aegean Sea from Turkey in October 2015. Hide Caption 2 of 26 Photos: Europe's migration crisis in 25 photos Hide Caption 3 of 26 Photos: Europe's migration crisis in 25 photos Migrants step over dead bodies while being rescued in the Mediterranean Sea, off the coast of Libya in October 2016. Agence France-Presse photographer Aris Messinis was on a Spanish rescue boat that encountered several crowded migrant boats. Messinis said the rescuers counted 29 dead bodies -- 10 men and 19 women, all between 20 and 30 years old. "I've (seen) in my career a lot of death," he said. "I cover war zones, conflict and everything. I see a lot of death and suffering, but this is something different. Completely different." Hide Caption 4 of 26 Photos: Europe's migration crisis in 25 photos Authorities stand near the body of 2-year-old Alan Kurdi on the shore of Bodrum, Turkey, in September 2015. Alan, his brother and their mother drowned while fleeing Syria. This photo was shared around the world, often with a Turkish hashtag that means "Flotsam of Humanity." Hide Caption 5 of 26 Photos: Europe's migration crisis in 25 photos Migrants board a train at Keleti station in Budapest, Hungary, after the station was reopened in September 2015. Hide Caption 6 of 26 Photos: Europe's migration crisis in 25 photos Children cry as migrants in Greece try to break through a police cordon to cross into Macedonia in August 2015. Thousands of migrants -- most of them fleeing Syria's bitter conflict -- were stranded in a no-man's land on the border. Hide Caption 7 of 26 Photos: Europe's migration crisis in 25 photos The Kusadasi Ilgun, a sunken 20-foot boat, lies in waters off the Greek island of Samos in November 2016. Hide Caption 8 of 26 Photos: Europe's migration crisis in 25 photos Migrants bathe outside near a makeshift shelter in an abandoned warehouse in Subotica, Serbia, in January 2017. Hide Caption 9 of 26 Photos: Europe's migration crisis in 25 photos A police officer in Calais, France, tries to prevent migrants from heading for the Channel Tunnel to England in June 2015. Hide Caption 10 of 26 Photos: Europe's migration crisis in 25 photos A migrant walks past a burning shack in the southern part of the "Jungle" migrant camp in Calais, France, in March 2016. Part of the camp was being demolished -- and the inhabitants relocated -- in response to unsanitary conditions at the site. Hide Caption 11 of 26 Photos: Europe's migration crisis in 25 photos Migrants stumble as they cross a river north of Idomeni, Greece, attempting to reach Macedonia on a route that would bypass the border-control fence in March 2016. Hide Caption 12 of 26 Photos: Europe's migration crisis in 25 photos In September 2015, an excavator dumps life vests that were previously used by migrants on the Greek island of Lesbos. Hide Caption 13 of 26 Photos: Europe's migration crisis in 25 photos The Turkish coast guard helps refugees near Aydin, Turkey, after their boat toppled en route to Greece in January 2016. Hide Caption 14 of 26 Photos: Europe's migration crisis in 25 photos A woman sits with children around a fire at the northern Greek border point of Idomeni in March 2016. Hide Caption 15 of 26 Photos: Europe's migration crisis in 25 photos A column of migrants moves along a path between farm fields in Rigonce, Slovenia, in October 2015. Hide Caption 16 of 26 Photos: Europe's migration crisis in 25 photos A ship crowded with migrants flips onto its side in May 2016 as an Italian navy ship approaches off the coach of Libya. Passengers had rushed to the port side, a shift in weight that proved too much. Five people died and more than 500 were rescued. Hide Caption 17 of 26 Photos: Europe's migration crisis in 25 photos Refugees break through a barbed-wire fence on the Greece-Macedonia border in February 2016, as tensions boiled over regarding new travel restrictions into Europe. Hide Caption 18 of 26 Photos: Europe's migration crisis in 25 photos Policemen try to disperse hundreds of migrants by spraying them with fire extinguishers during a registration procedure in Kos, Greece, in August 2015. Hide Caption 19 of 26 Photos: Europe's migration crisis in 25 photos A member of the humanitarian organization Sea-Watch holds a migrant baby who drowned following the capsizing of a boat off Libya in May 2016. Hide Caption 20 of 26 Photos: Europe's migration crisis in 25 photos A migrant in Gevgelija, Macedonia, tries to sneak onto a train bound for Serbia in August 2015. Hide Caption 21 of 26 Photos: Europe's migration crisis in 25 photos Migrants, most of them from Eritrea, jump into the Mediterranean from a crowded wooden boat during a rescue operation about 13 miles north of Sabratha, Libya, in August 2016. Hide Caption 22 of 26 Photos: Europe's migration crisis in 25 photos Refugees rescued off the Libyan coast get their first sight of Sardinia as they sail in the Mediterranean Sea toward Cagliari, Italy, in September 2015. Hide Caption 23 of 26 Photos: Europe's migration crisis in 25 photos Local residents and rescue workers help migrants from the sea after a boat carrying them sank off the island of Rhodes, Greece, in April 2015. Hide Caption 24 of 26 Photos: Europe's migration crisis in 25 photos Investigators in Burgenland, Austria, inspect an abandoned truck that contained the bodies of refugees who died of suffocation in August 2015. The 71 victims -- most likely fleeing war-ravaged Syria -- were 60 men, eight women and three children. Hide Caption 25 of 26 Photos: Europe's migration crisis in 25 photos Syrian refugees sleep on the floor of a train car taking them from Macedonia to the Serbian border in August 2015. How to help the ongoing migrant crisis Hide Caption 26 of 26

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.