While details were sketchy, the leaders agreed in principle, at least, on how to shore up their external borders and create screening centers for migrants, to decide more quickly whether or not they are legitimate refugees.
Speaking to reporters at 5 am (0300 GMT), she said it was a good signal that leaders had been able to agree a common text, but acknowledged the bloc still had "a lot of work to do to bridge the different views".
With the EU bloc deeply divided over migration, with some member states more directly affected than others, several Central European states have rejected an EU scheme which would seek to relocate 160,000 refugee camps in Greece and Italy, of which are vastly overcrowded.
Will the deal stop migrants arriving?
On the island of Malta, meanwhile, screening began on Thursday for 234 people who spent almost a week at sea on a humanitarian rescue vessel, to determine whether they are eligible for asylum and relocation to one of eight European Union nations. However, according to CNN, some eastern European countries, have fiercely resisted mandatory quotas for EU nations to take in refugees.
When the incidents at sea were unfolding, the European Commission claimed that it lacked competence to ensure the migrants being rescued by the Italian national coast guard in charge of search and rescue operations in the area. They go into the room, clash, storm out, go back again, clash again.
Like the "controlled centers" inside the European Union, the poposed "regional disembarkation platforms" outside the European Union are tasked with distinguishing migrants "in full respect of global law and without creating a pull factor".
"A consensus must be found on the Dublin Regulation so that it is reformed on the basis of a balance between responsibility and solidarity", the agreement said of a reform that has been bogged down for years. "We are satisfied. Today Italy is no longer alone".
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Following the win, Manchester United defender Marcos Rojo revealed his half-time speech spurred them on to win. A draw would have been enough for the West African side to progress to the knockout stage of the tournament.
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German Chancellor Angela Merkel told reporters the European Union still had "a lot of work to do to bridge the different views". "France is not a country of first arrival". He has threatened to start turning away migrants who have already registered elsewhere from the border in his home state.
But the political tremors are still being felt across Europe, with populist, anti-immigrant parties on the rise in many countries.
After allowing more than one million asylum seekers into Germany since 2015, Dr Merkel faces an end-of-month deadline from her own interior minister to curb so-called secondary migration.
It took place in an atmosphere of political crisis, with German Chancellor Angela Merkel under intense political pressure at home to take a firmer stance on migration.
"I did not undersign any specific agreement with Merkel" on taking back migrants, he added.
Ms. Merkel is fighting a battle at home and overseas against critics who accuse her of endangering European security with her welcoming approach to migrants.
But apparently that is not enough and the Council is determined to "reinforce this policy to prevent a return to the uncontrolled flows of 2015 and to further stem illegal migration on all existing and emerging routes". "Some may think I am too tough in my proposals on migration, but trust me", he said.
The Taoiseach has previously called for border security to be stepped up in response to the growing challenges posed by migrants crossing from Africa to Italy. Such a move would have ripple effects far beyond Germany, she warned, endangering the European project of border-free travel.