Sixteen of the EU's 28 leaders held talks in Brussels on Sunday, ahead of a summit, the European Council, on June 28-29.
Spain's Prime Minister Pedro Sanchez said his country is committed to a joint European response on illegal migration.
Mrs Le Pen added French President Emmanuel Macron and Mrs Merkel, his top EU ally, had "isolated themselves on the European scene" due to their soft approach on illegal immigration.
After the summit, Mr Conte said it had gone well and "we are all pulling in the right direction".
"Our public opinion is asking for this", Italian Prime Minister Giuseppe Conte said when arriving for the talks, adding he would propose his new ideas on migration.
Discussions are set to continue over a formal European Union summit of the bloc's 28 leaders in Brussels on Thursday.
The ship had rescued the migrants, including children and pregnant women, on Thursday but Malta and Italy initially refused to take them in. Reflecting the mounting anger over the lack of assistance from its partners, Italy's new government has refused to admit foreign-flagged rescue ships, accusing them of abetting traffickers.
Macron also riled Italy, the main landing point for African migrants, by saying that the migration emergency, which peaked in 2015, had passed and was now mainly a political issue.
They may be the highest for Chancellor Angela Markel of Germany, which has taken in the lion's share of asylum-seekers.
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It comes amid pressure back home, which is threatening Merkel's ruling coalition.
And despite the decline in arrivals, the political consequences of migration pressures are still reverberating across Europe.
The open challenge against Merkel is led by CSU boss and Interior Minister Horst Seehofer, who has cultivated ties with anti-immigration hardliners in Austria, Hungary and Italy.
There was also some support for screening African migrants heading to Europe in North Africa and the Balkans, an idea that has sparked some concern about migrant rights, particularly after a 2016 European Union migrant deal with Turkey.
An EU government official told reporters that Rome won't discuss a deal with Merkel on secondary migration between member-states unless it's part of a comprehensive package spreading responsibility for handling incoming protection seekers from frontline countries to the entire bloc. "So instead of looking inwards, they look outwards". Spain has seen a sharp rise in migrant arrivals. Under current rules, an European Union country is responsible for processing the asylum claims of all new arrivals, which has put enormous pressure on Mediterranean states, especially Italy and Greece. In 2017, for example, Germany received almost a quarter-million requests for refugee status and Italy almost 130,000 - compared to just over 5,000 for Poland. The refugees were allowed to dock in Valencia and claim asylum in Spain. "Schengen is at risk", the document said.
The ship eventually docked in a Spanish port after being turned away by Italy, whose new right-wing, populist coalition government has taken a hardline stance on immigration, as promised on the campaign trail.
The issue was raised during a meeting at the Vatican Tuesday between Macron and Pope Francis, who has called for "solidarity" with migrants.
It follows a heated exchange between Emmanuel Macron and Italy's new interior minister Matteo Salvini, who accused the French president of being arrogant and drinking too much champagne.
Meanwhile, the migrants themselves remained front and center in European news Sunday, as one humanitarian vessel remained stranded at sea in search of a safe harbor.
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