Conte, whose government includes the anti-establishment 5-Star movement and far-right League, had earlier refused to endorse a summit text on security and trade until other leaders had pledged to help Italy manage Mediterranean arrivals.
The leaders also agreed that some European countries would establish centers within their own borders to process migrants seeking asylum after their arrived in the continent.
Italy had threatened to veto any deal if fellow European Union leaders failed to do more to help the country, where a large share of incoming migrants and refugees arrive.
Conte blocked the summit conclusions in a bid to get his reluctant counterparts to share responsibility for asylum seekers landing on Italian shores.
German Chancellor Angela Merkel has drawn up a raft of measures to tighten controls on the influx of migrants, according to a document submitted to her coalition partners Saturday as she battles for political survival, reported AFP.
Leaders agreed that "controlled centres" should be set up in member states on a voluntary basis for "rapid and secure" processing to distinguish between irregular migrants and refugees eligible for asylum.
European Union leaders declared victory yesterday, claiming to have set aside major differences over how best to handle migrant arrivals as they commissioned new plans to screen people in North Africa for eligibility to enter Europe. In 2015, more than a million refugees and migrants arrived in Europe.
In recent weeks, vessels with rescued migrants and refugees on board have been left stranded in the Mediterranean after they were barred from docking.
If she failed to reach an agreement that would allow her to turn back certain groups of migrants at the German border, the Bavarians could quit her government, a move that would most likely put her out of a job after nearly 13 years as German leader and usher in months of uncertainty in the European Union's most influential country.
European Union (EU) leaders have chosen fear over compassion by signing off Council Conclusions which could harm some of the world's most vulnerable men, women and children, Amnesty International said today.
In this respect, the conclusions state that future transfers will be made on a voluntary basis, distinguishing between irregular migrants, who will be returned, and those in need of worldwide protection, for whom the principle of solidarity would apply.
"I do sympathise with Italy - they are facing the whole burden", he said, but he also urged Conte to be sensitive to the pressures facing other leaders, particularly on migrants' movements within the EU.
Austrian Chancellor Sebastian Kurz shared Orban's opinion about the solution, "We have always been calling for these protected areas, safe zones, landing centers, however one wants to call them, outside of Europe ― this idea has now prevailed".
This is nearly six times less than in 2016 over the same period, following a peak in arrivals in 2015, and approximately 30 percent of those arriving on European shores needed global protection.
"Europe is really rolling the dice", said Jill Goldenziel, an associate professor at the Marine Corps University, who is writing a book on the global migration crisis.
The agreement further calls for efforts to break up people smuggling operations, and to be more aggressive in returning refugees who do not qualify for asylum.
The majority of people in Central, Eastern and Southern European countries are opposed to migration and see an importance in preserving Christian culture, according to a new survey conducted by Nézőpont Institute.