The French and German leaders have urged EU members to act together to tackle the migrant crisis which has seen more than 600,000 people arrive in the bloc during 2015.
French President Francois Hollande and German Chancellor Angela Merkel called for a revamped system for dealing with asylum claims.
They spoke during a joint address to the European Parliament in Strasbourg.
The migrant crisis has seen EU states at odds on how to deal with the influx.
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Both leaders agreed that said the often-flouted current rules – requiring asylum claims to be lodged in the first EU nation reached – were obsolete.
And they said the only way to tackle the problem was for the EU to work together – on trying to end conflict in the regions affected; on supporting countries like Turkey, which is currently home to two million Syrian refugees; and in providing a safe haven for refugees.
It was the first joint speech to the European Parliament by the leaders of France and Germany since President Francois Mitterrand and Chancellor Helmut Kohl in 1989.
There were dissenting voices, including Nigel Farage, the leader of the United Kingdom Independence Party (UKIP), who accused the pair of creating a “virtually a stampede” of refugees.
Mrs Merkel told European MPs that the influx of refugees was “changing the agenda in Europe… global events affect us whether we like it or not”.
“We have to recognise that even if we tried to seal ourselves off completely, even at the price that people could suffer at our borders, that would help no-one.”
People would find a way to get to Europe whatever the barriers, she insisted, adding: “Sealing and cordoning yourself off in the age of the internet is an illusion. No problem would be solved, additional and serious problems would arise.”
Germany has taken in far more migrants than any other EU nation, while others have refused to sign up to a quota system.
“In the refugee crisis, we must not succumb to the temptation of falling back into national action. Quite the contrary, now we need more Europe,” Mrs Merkel said.
On the migrants arriving in Europe, she said: “We must see them as people, whether they have the prospect of remaining or not. Humanitarian standards of accommodation and claim processing must be upheld.”
‘End of Europe’
Mr Hollande admitted Europe had initially been “slow in understanding that the tragedies of the Middle East and Africa would have consequences for Europe itself”.
The EU now needed to work together in solidarity, rather than retreating into “our own national shells”, he said, adding that it would be a “tragic error” to back away from open borders.
“There is a humanitarian crisis which we need to confront, with an influx of refugees… The only solution is a strong Europe.
“We need not less Europe but more Europe. Europe must affirm itself otherwise we will see the end of Europe, our demise.”
In response, UKIP’s Mr Farage said: “In what must count as perhaps the worst piece of public policy seen in modern Europe for half a century… you compounded the already failing and flawed EU common asylum policy by saying to the whole world: ‘Please come to Europe.’
“And we saw, frankly, virtually a stampede. And we learn that 80% of those who are coming are not Syrian refugees.
“In fact, what you’ve done is to open the door to young, male economic migrants – many of whom behave in a rather aggressive manner, quite the opposite of what you’d expect from any refugee.”