German Chancellor Angela Merkel has said that European Union states "must share the responsibility for refugees seeking asylum," arguing that failing them will betray the bloc's values.
At a news conference in Berlin on Monday, Merkel pressed once again for quotas to spread asylum-seekers out among more countries in the 28-nation grouping.
"If Europe fails on the question of refugees, this close connection with universal civil rights ... will be destroyed and it won't be the Europe we want," she said.
Hungary, Slovakia, the Czech Republic and Poland have all sought to block the influx of refugees.
Merkel was openly critical of the idea voiced by Slovakia on giving priority to refugees who are Christian.
The chancellor said that Europe's values are based on the dignity of every individual, and that saying Muslims are not wanted "can't be right".
Hungary is building a four-metre high fence on its southern border with Serbia to try to stop refugees coming across the Balkans.
Trains to Germany
On Monday, hundreds of refugees stranded in Budapest, the Hungarian capital, boarded trains to Germany via Austria as the Hungarian authorities apparently failed to enforce visa rules.
Two trains were stopped in the Hungarian town of Hegyeshalom at the border with Austria, where Austrian police prevented those who had already applied for asylum in Hungary from travelling on.
Roman Hahslinger, the Vienna police spokesman, told the DPA news agency that Austrian officers had no effective means to stop other refugees if they plan to travel to Germany or another EU state, even if they are legally obliged to stay in Austria for two weeks under immigration rules.
Why Al Jazeera will not say Mediterranean 'migrants'
Al Jazeera's Andrew Simmons, reporting from Hegyeshalom, said the refugees were "overjoyed" to be able to travel on.
Simmons said it was creating confusion, but there were speculations that Germany and Hungary were in contact to clear it up.
German police in Rosenheim near the Austrian border said that they would no longer frisk incoming trains.
Germany has said it will accept all asylum applications from Syrians instead of sending them back to the first EU state they entered, which is required by EU law.
Hungary accused Berlin of creating confusion with leniency towards Syrians.