Hundreds of refugees arrived in Austria's capital Vienna and the German city of Munich late on Monday, Al Jazeera reported, citing witnesses.
Nearly all the refugees, whose the main routes are through Turkey or Greece, the Balkans and EU countries, are fleeing from civil wars in Syria, Iraq and Afghanistan.
According to passengers on the trains, Austrian authorities seemed to have given up on applying EU rules by filtering out refugees who had already claimed asylum in Hungary.
They also said Austrian authorities have also not intervened against refugees arriving in Vienna and the police are acting passively.
A 33-year-old refugee from Kobani, Syria, named Khalil - who was working as an English teacher and bought a ticket in Budapest to travel to Hamburg with his wife and ill baby daughter - said, "Thank God nobody asked for a passport ... No police, no problem,” Reuters reported.
Meanwhile, on Monday, around 40 refugee caught by police were asked to accompany them to be registered on a train that was traveling from Vienna to Passau, Germany.
On the other hand, the UN’s High Commissioner for Refugees (UNHCR) on Wednesday called on European states to work together to come up with a working strategy that could manage and equally distribute the massive daily influx of refugees escaping the violence in their home countries across the nations of the EU without violating their human rights as refugees and asylum seekers.
The UNHCR said that all European countries along with the EU must help in providing support to Greece, Macedonia and Serbia whose capacities have been overstretched by the sheer number of refugees making their way through Europe.
On the other hand, Turkey, the country worst affected by the refugee influx, has received 2 million refugees and spent $5.6 billion on hosting them - more than any other country - according to Turkish authorities.
German Chancellor Angela Merkel praised Turkey on Monday for providing shelter to millions of refugees.
"Turkey has done a lot so far to address the Syrian refugee problem and continues to do so… but recent developments and refugees coming to Greece show that Turkey has also come to its limits of what it can achieve alone," Merkel said at a Berlin news conference.
Merkel also warned that failure to resolve the crisis could undermine the EU.
“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,” Merkel told reporters in Berlin.
"If we don't succeed in fairly distributing refugees then of course the Schengen question will be on the agenda for many," she also said.
"We stand before a huge national challenge. That will be a central challenge not only for days or months but for a long period of time."
In August, Germany revised its estimate for the total number of estimated refugees it has received 450,000 to 800,000, meaning it holds more refugees than any other country in the EU.