The president of the European Council has warned that the migrant crisis could threaten the cohesion of the EU.
Donald Tusk told the European Parliament the challenge was the biggest the EU had faced for a decade.
Meanwhile Parliament President Martin Schulz accused European governments of putting national interests above finding solutions as a community.
The UN’s refugee agency (UNHCR) says more than 700,000 migrants have reached Europe by boat so far this year.
EU leaders have exchanged angry accusations as authorities struggle to cope with the thousands of new arrivals, many of them refugees from Syria and other conflict zones.
‘Tectonic changes’
Speaking in Strasbourg, President Tusk said the crisis threatened to transform the EU and destroy principles such as border-free travel between Schengen zone countries.
“This challenge has the potential to… cause tectonic changes in the European political landscape,” he said.
“These are not changes for the better.”
Image copyright Reuters Image caption European Council President Donald Tusk said he did not want to think of the alternative if member states failed to handle the crisis together
Mr Tusk said these were “extraordinary times” that required “extraordinary measures, extraordinary sacrifices and extraordinary solidarity”.
His warning comes after European leaders held an emergency summit in Brussels to discuss how to handle growing numbers of migrants.
Slovenia’s police said on Monday that nearly 10,000 migrants had arrived from Croatia in the past 24 hours.
More than 9,000 migrants arrived in Greece every day last week – the highest rate so far this year.
Deliver on commitments
Despite agreements on boosting the number of reception centres and deploying more police officers, European Parliament President Schulz said he left the talks feeling “deeply worried”.
“Promises are being made and they’re not delivered upon,” he said.
“Governments of the right and of the left sometimes think national interests are more important than community solutions. What suffers are the refugees and the cohesion of the European Union.”
Jean-Claude Juncker, President of the European Commission which called Sunday’s summit, said the need for a meeting to encourage discussion between member states showed the EU was “not in good shape”.
He urged member states to deliver on commitments made – including producing extra money – claiming they were “moving slowly when they should be running”.
Staggering increase
Europe is still struggling to find a unified approach to the hundreds of thousands of people arriving on its shores, but delays in Brussels are not slowing down the migrants and refugees, reports the BBC’s Imogen Foulkes in Geneva.
The latest figures from the UNHCR – showing that more than 700,000 people have reached Europe via the Mediterranean this year – mark a staggering increase on last year, our correspondent says.
In the whole of 2014 the number of people arriving was 219,000.
The UNHCR says most arrivals are not economic migrants, but people fleeing war and persecution.
The conflict in Syria continues to be the biggest driver of the migration.