The Austrian chancellor has indicated that the country could begin closing its borders again after two days of unprecedented refugee arrivals from eastern Europe.

Werner Faymann said that emergency measures agreed by Austria and Germany to accept large numbers of refugees from Hungary should be lifted “gradually”.

Bavarian state officials have said that a total of 6,800 refugees entered Germany via Austria on Saturday, with another 5,000 expected on Sunday.

In a statement following what he described as “intensive talks” with Germany’s Angela Merkel and a telephone call with the Hungarian prime minister Viktor Orban, Mr Faymann said: “We have always said this is an emergency situation in which we must act quickly and humanely.

“We have helped more than 12,000 people in an acute situation. Now we have to move step by step away from emergency measures towards normality in conformity with the law and dignity.”

Around 700 who were able to get on board two trains to Munich were welcomed early on Sunday by a dozen or so volunteers handing out chocolate. More were expected later, a regional official said, and most were given medical checks before being taken to reception centres.

Cars of Austrian volunteers willing to transport refugees to Austria enter Hungary at the former border station of Hegyeshalom (EPA)

Refugees arrive at the train station in Salzburg, Austria, with many of them journeying onwards to Germany (EPA)

Many more crossed the border by other means, and the Hungarian government put on around 100 buses to help get people to the Austrian border. A convoy of around 140 cars and vans filled with food and water left Vienna on Sunday to provide for the column of marchers, and collect those less able to walk.

Munich’s mayor, Dieter Reiter, said on Sunday that he was not worried about the numbers arriving in the city – only “how can we give them a feeling that they are safe here”.

But even in a city which has been among those most praised for its positive reaction to the influx of refugees, concerns were being raised.

Refugees march from Hungary to Austria Show all 10 1 /10 Refugees march from Hungary to Austria Refugees march from Hungary to Austria Refugees march from Hungary to Austria Migrants walk in a long line along the highway near Budapest, Hungary, Friday, Sept. 4, 2015 AP Refugees march from Hungary to Austria Refugees march from Hungary to Austria Migrants walk on the railway tracks between Bicske and Szar, some 40 km west of Budapest, Hungary, 04 September 2015 EPA Refugees march from Hungary to Austria Refugees march from Hungary to Austria The destination for most of those walking is reportedly Austria AP Refugees march from Hungary to Austria Refugees march from Hungary to Austria Most refugees have come to Hungary through the southern border with Serbia AP Refugees march from Hungary to Austria Refugees march from Hungary to Austria People walk in a long line along the highway near Budapest, Hungary AP Refugees march from Hungary to Austria Refugees march from Hungary to Austria Over 150,000 people seeking to enter Europe have reached Hungary this year AP Refugees march from Hungary to Austria Refugees march from Hungary to Austria Refugees walk along Budaorsi Street on their way out of Budapest EPA Refugees march from Hungary to Austria Refugees march from Hungary to Austria Refugees hold up an EU flag as they on the highway out of Budpest AP Refugees march from Hungary to Austria Refugees march from Hungary to Austria Refugees exit Budapest AP Refugees march from Hungary to Austria Refugees march from Hungary to Austria Hundreds of migrants walk after leaving the transit zone of the Budapest main train station AFP

Simone Hilgers, a spokesperson for the authorities in Upper Bavaria, Germany’s largest state, told the Associated Press: “Munich and Bavaria can't manage it alone. [We] need the support pledged by other [German] states.”

Germany alone expects to receive 800,000 refugees by the end of 2015 – roughly 1 per cent of its population, and by far the greatest contribution to the crisis from any EU member state.

The numbers arriving in Europe are nonetheless a relatively small proportion of the four million estimated to have fled Syria since its civil war began in 2011, amid warnings that millions more could be displaced.