German Chancellor Angela Merkel has warned that the migrant crisis will not be solved imminently, and its handling will shape Europe in the long term.
She told German MPs the latest EU measures agreed on Wednesday were only a "first step" and that "selective relocation" of migrants was not enough.
The flow of migrants over Europe's borders continues. Hungary announced a record 10,046 arrivals on Wednesday.
Rows among nations also continue - the latest between Serbia and Croatia.
The European Commission has meanwhile warned that a failure to address the crisis properly could lead to a surge in right-wing extremism across Europe.
About half a million migrants have arrived in Europe this year, exposing deep divisions within the EU.
'Millions of refugees'
Mrs Merkel told the German parliament: "I am deeply convinced that what Europe needs is not just selective relocation [of migrants], but a permanent process for fairly distributing refugees among member states.
"A first step has been taken, but we are still far from where we should be."
What the EU leaders agreed
- At least €1bn (£700m, $1.1bn) extra will be donated to the UN refugee agency and the World Food programme
- More help for Lebanon, Jordan, Turkey and other countries
- Greater co-operation and dialogue with Turkey
- Assistance for Balkan states, who have become a major route for migrants travelling north
- Strengthened border controls, including more funding for border security forces
- Further summit scheduled for October. Talks to include Turkish President Recep Tayyip Erdogan
On Tuesday, EU ministers backed mandatory quotas to divide up 120,000 refugees among members - but the vote was passed only by majority and was fiercely opposed by some nations. Slovakia has launched a legal challenge.
Mrs Merkel welcomed the EU measures to improve border controls and establish proper registration of migrants at entry points in Greece and Italy.
She said the participants at Wednesday's EU leaders' summit had "recognised the scale of the problem and sent a signal of unity".
But she warned that "the way we tackle the crisis will shape Europe in the long term" and criticised the failure of some EU states to meet the "minimum standards in Europe for the accommodation and care of refugees".
Mrs Merkel vowed to speed up asylum procedures in Germany.
Later on Thursday, she was meeting the leaders of Germany's 16 states in Berlin to discuss funding for handling migrants and speeding up asylum claims.
She insisted "the opportunities are much bigger than the risks".
But Mrs Merkel said the EU also needed help from outside the EU, calling for the support "of our transatlantic partners, the United States, as well as with Russia and the states of the region of the Middle East".
After Wednesday's summit, European Council President Donald Tusk warned that the "greatest tide of refugees and migrants is yet to come".
"We should be talking about millions of potential refugees," he said, adding: "We need to correct the policy of open doors and windows."
The flow has continued unabated, with Hungary recording a record number on Wednesday - 9,939 entering from Croatia and 102 from Serbia.
It was Hungary's introduction of tough new laws on its border with Serbia last week that led to thousands of migrants diverting to Croatia.
This has led to increased tension between Serbia and Croatia. Serbia has banned Croatian cargo traffic and Croatia in return has now banned Serbian-registered vehicles.
Croatia said reports that individual Serbian citizens had also been barred from entering Croatia were incorrect, saying there had only been "a problem with passports".
But Serbia condemned Croatia, saying its border restrictions were "comparable only to those of the World War Two fascist regime".
Hungary's fairly smooth processing of migrants arriving from Croatia may well change in the coming days when it is expected to complete a razor-wire fence on its Croatian border.
Hungary has also begun constructing a razor-wire fence along its border with Slovenia - believed to be the first such barrier between members of the EU's Schengen zone.
The zone's provision of loose border controls and passport-free travel between its members has been tested by the migrant crisis.
Meanwhile, European Commission Vice-President Frans Timmermans warned of dire consequences if border checks were not properly enforced.
He told the BBC: "If we're not able to tackle this issue, if we're not able to find sustainable solutions, you will see a surge of the extreme right across the European continent."
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.
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