Though arrival numbers have always been decreasing and are now low, migration has shot back to the top of Europe's political agenda also because German Chancellor Angela Merkel's coalition partner issued an ultimatum for an EU-wide deal on migration.
Earlier, Bild newspaper, citing unnamed sources from the CSU leadership, reported that the CSU would give Merkel two weeks, until an EU summit on June 28-29, to deliver a European solution on migrant policy before defying her by implementing his plan.
The EuroStoxx 50 index fell 1.25% and the German DAX index finished the day 1.51% lower on Monday 18 June, as this new worry exacerbated existing investor concerns over the region.
Hardliners in her conservative bloc want to bar asylum-seekers from entering Germany if they've already applied or registered for asylum in other European countries.
Conte, who was visiting Germany for the first time since assuming office on June 1, said Italy wanted changes to European Union immigration rules to ensure other European Union countries share the burden of handling refugees.
In Germany, voters in September's election handed veteran leader Merkel her worst score ever, giving seats for the first time to the far-right anti-Islam AfD. The shocking case of a 14-year-old Jewish girl, Susanne Feldman, who was raped and murdered, has provoked alarm, even among supporters of an open immigration policy.
White House Deputy Press Secretary Hogan Gidley echoed the president's argument in an interview with FOX Monday, contrasting the permanent separation caused when a loved one is killed to the "temporary separation of families".
For all the noise, the CSU knows that there is more at stake.
"Seehofer has the majority of the people behind his position, as well as big sections of Merkel's CDU and all of his CSU", observes political scientist Heinrich Oberreuter.
"We just want to finally have a sustainable solution to send refugees back to the borders".
If Seehofer, backed by his CSU, were to defy her by enforcing the plan on Monday, Merkel would be nearly certainly forced to fire him.
By contrast, Merkel has warned of a resulting domino effect as Germany's neighbors rush to shutter their internal Schengen borders and is calling for a joint European solution to the "refugee crisis" to be reached within the next two weeks.
Over the weekend Seehofer had signalled he would hold off on implementing the measure until after an European Union summit on migration and asylum policy that is scheduled for the end of the month.
"The situation is serious but still solvable", he wrote. If he does, that would threaten the government.
Central and eastern European Union nations such as Hungary and Poland have either refused outright or resisted taking in refugees under an European Union quota system that has essentially floundered.
Here's the paradox: Italy and Austria both have anti-immigrant governments.
Mrs Merkel is in the middle of a serious domestic row after defending her country's immigration policy.