Conte's own anti-establishment government had a separate dispute with French President Emmanuel Macron earlier in the week after Italy's anti-immigration interior minister, Matteo Salvini, refused to allow a ship carrying more than 600 migrants and operated by a charity organization to dock at an Italian port.
"If the Bavarian CSU does not agree to any compromise on migration policy, her current government may fall apart shortly".
Now, however, Italy's new anti-establishment government has demanded that Europe does more to help it handle refugees and migrants arriving from across the Mediterranean.
Italy wants to adapt current European Union asylum guidelines in favour of "a new approach that is more harmonious, so that whoever sets foot in Italy, sets foot in Europe", Conte said.
"Crime in Germany is up 10% plus (officials do not want to report these crimes) since migrants were accepted", Trump said in his latest tweet.
The proposals he will discuss when he sits down with German Chancellor Angela Merkel outside Berlin on Tuesday will be far less ambitious, with deep differences between the two European powerhouses.
However, Mr. Trump's claim that Germans were turning against their leaders because of an increase in crime spurred by immigration was easily debunked by a report last month from Mr. Seehofer's own ministry showing a almost 10% drop in crime past year, to the lowest point since 1992. "More EU centralisation, this is not what voters want", tweeted former UKIP leader and MEP Nigel Farage, reacting to the news Tuesday afternoon.More news: Protest held at Courthouse in opposition to Trump administration's border actions
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Merkel is now locked in a stand-off with her party's Bavarian allies - the Christian Social Union, led by Interior Minister Horst Seehofer - over the government's migration policy. The CSU exists only in Bavaria, and the CDU in Germany's other 15 states.
The CSU leadership agreed at a meeting in Munich to delay introducing their entry ban until after a June 28-29 European Union summit, allowing Merkel time to seek an EU-wide solution.
Noting in their declaration that "the EU faces existential challenges", the leaders agreed to set up a European border police and to create a European asylum office.
Merkel and Macron have both stressed that, as US President Donald Trump openly challenges the European Union with a trade war and over security and climate policy, the bloc must learn to stand its ground on the world stage.
The EU could take steps to stop asylum seekers moving on from the country in which they are registered and start deciding asylum requests at centres to be established beyond EU borders in the future, according to a draft summit statement.
German Interior Minister Horst Seehofer, left, talks to Chancellor Angela Merkel in parliament.
The EU has given aid and money to countries from Turkey and Jordan to Libya and Niger. We see states that are turning inward, trying to find national solutions to problems that require European solutions.
Since peaking in 2015, the migrants' use of the Balkan route toward Western Europe has been impaired in part by Hungary's construction of razor-wire fences on its southern borders.