Britain will resist demands for a European Union-wide migrant quota as ministers meet for an emergency summit to discuss the crisis.
Home Secretary Theresa May is joining counterparts in Brussels in the latest effort to agree a co-ordinated response to the upsurge in arrivals on Europe's borders.
Germany upped pressure for a deal on the eve of the talks by imposing border controls amid warnings regions were struggling to cope with large numbers fleeing the war in Syria.
The temporary suspension of the border-free Schengen Agreement came after more than 14,000 arrived at Munich station in response to Chancellor Angela Merkel's decision to allow free access to unregistered migrants gathering in Hungary.
Interior minister Thomas de Maiziere said the move was "also a signal to Europe: Germany is facing up to its humanitarian responsibility, but the burdens connected with the large number of refugees must be distributed in solidarity".
The United Nations High Commissioner for Refugees urged the EU to move to "the rapid implementation of a relocation programme" to spread refugees among all EU countries - a move resisted by many member states.
Prime Minister David Cameron has made clear that Britain will not participate in European Commission plans to redistribute 160,000 migrants around the continent from Italy, Greece and Hungary.
He has said the UK will take in 20,000 Syrians but only from camps in the region, arguing that focusing on migrants who have already reached Europe would merely encourage more to come.
The temporary reintroduction of border controls was seen as a serious blow to the survival of the Schengen Agreement under which 26 European countries, mostly in the EU, have no border controls and operate a joint asylum policy.
Mrs May has blamed scenes of drowned migrants on a "broken European migration system", saying the tragedies such as the dozens of refugees found dead in the back of an abandoned lorry "have been exacerbated by the European system of no borders, the Schengen area, in which the UK has never taken part."
Ukip leader Nigel Farage said: "By shutting the border with Austria, it is clear that the German government have realised the scale of their error. Schengen surely can't survive now."
David Miliband, who is visiting the Greek island of Lesbos near where another 28 migrants drowned yesterday on a makeshift boat trying to make the journey to Europe from Turkey, criticised the UK response.
The former foreign secretary,who now heads up the aid agency International Rescue Committee (IRC),described David Cameron's commitment to take in an average of 4,000 Syrian refugees a year as the equivalent of the number arriving on the beaches of Lesbos every day.
"The EU has an opportunity to move beyond its fragmented and lacklustre response to date and finally acknowledge the severity of this humanitarian crisis," he said.
"Each country needs to shoulder the burden and agree to both relocate refugees who have reached the continent and resettle the most vulnerable from the Middle East."