Instead of hard overall deals among all member states, she said it was "also about bi- and trilateral agreements for mutual benefit".
The unity of the heads of the interior Ministry of Italy, Germany and Austria's migration policy Kurtz has called the "axis of freedom" (or "axis of the willing" - the axis of willing) and announced further cooperation between the three countries on this problem.
Mr Sanchez urged the European Union partners to help Spain deal with the arrival of thousands of migrants from Africa.
Merkel's ally in pursuit of European solidarity on migration, French President Emmanuel Macron, threatened non-compliers with economic sanctions ahead of the meeting, saying the EU can not have members, which "benefit hugely from EU solidarity and claim national self-interest when it comes to the issue of migrants".
"Once on European soil, we are in favour of setting up closed centres in accordance with the UNHCR (United Nations High Commissioner for Refugees).so that each country takes people who are entitled to asylum in an organised way", Macron said.
Merkel's open-door migrant policy, which has resulted in the arrival of more than 1.6 million migrants in Germany since the start of 2015, is widely blamed for the rise of the far-right Alternative for Germany (AfD). He has also said that he favors punishing member states that do not show solidarity on the migrant issue. France's Macron also supported the idea of members acting in smaller groups.More news: Argentina take player power to new level ahead of Nigeria clash
"Going back to Rome satisfied", Italian Prime Minister Giuseppe Conte said in a tweet.
The proposal, seen by this website, broadly aims to stop people from ever reaching Italy and Europe by shoring up borders and outsourcing asylum.
European Union leaders also discussed measures to strengthen the external borders - an issue on which there is consensus - and proposals for centres in countries outside the bloc to separate genuine war refugees from economic migrants.
His appeal came as migration tensions surged on the Mediterranean itself.
The vessel - named Lifeline and operated by the German aid group Mission Lifeline - is now in Maltese waters with 224 people on board whom its crew pulled from the Mediterranean.
"The European Council will not yet provide an overall solution to the migration problem", Merkel said conceding a lack of consensus among EU members.More news: James Harden wins his first NBA Most Valuable Player award
Proactiva says Italy is seeking to have the Libyan coast guard conduct the rescues and bring the migrants back to North Africa.
Italy, which lies close to Libya, has taken in 650,000 boat migrants since 2014.
Malta's home affairs minister, Michael Farrugia, and Italy's transport minister, Danilo Toninelli, engaged in a Twitter war of words on Sunday over which country was being more "inhuman" about the fate of the Lifeline and its passengers.
Leaders appeared to agree on the need to shore up external borders, expand the EU's border agency Frontex, and increase efforts in African states to prevent people from reaching Libya to take boats towards Italy.
And a private cargo ship, the Alexander Maersk, has been waiting to be assigned a port since it picked up 113 migrants off southern Italy on Friday, the ship owner said.
Maltese Premier Joseph Muscat sought to lower the rhetoric as he arrived on Sunday in Brussels, saying now was not the time for a "blame game".
Like everything to do with migrants in Europe lately, even this meeting is proving controversial.More news: Trump says N.Korea still a nuke threat
Staying away are the hard-line leaders of Hungary, Poland, the Czech Republic and Slovakia, who have for years opposed migration.