The Trump administration wants to persuade four more countries to leave the European Union to “Make Europe Great Again”, according to reports of a longer, still-classified version of the US national security strategy released last week.

There are also suggestions of creating a new elite C5, or Core Five, forum of world powers to sideline the G7, comprising America, China, India, Japan and Russia.

The four EU countries seen as targets to follow Brexit are Austria, Hungary, Italy and Poland, according to leaked details reported by the US defence website Defense One.

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The classified version of the strategy, which warned of “civilisational erasure” in Europe because of mass immigration and multiculturalism, is believed to call for the US to “support parties, movements, and intellectual and cultural figures who seek sovereignty and preservation/restoration of traditional European ways of life … while remaining pro-American”.

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The US should “work more with” the four countries with traditions of dissent against the EU “with the goal of pulling them away from the [European Union]”, the document is believed to say.

Hungarian Prime Minister Viktor Orban at a joint press meeting.

Viktor Orban, the prime minister of Hungary, in Istanbul this week. Below, Giorgia Meloni, the Italian prime minister

SERHAT CAGDAS/ANADOLU VIA GETTY IMAGES

Italy's Prime Minister, Giorgia Meloni waits for Prime Minister of Bulgaria Rosen Zhelyazkov.

FILIPPO MONTEFORTE/AFP VIA GETTY IMAGES

The White House denied the existence of any version of the national security strategy other than the published one. Anna Kelly, a spokeswoman, told Defense One: “No alternative, private, or classified version exists. President Trump is transparent and put his signature on one NSS that clearly instructs the US government to execute on his defined principles and priorities.”

Trump has mused about Russia or China joining the G7, the group of the seven most advanced economies of democratic countries, which is made up of Britain, Canada, France, Germany, Italy, Japan and the US, with the European Union participating.

The secret US strategy is said to propose a C5 to meet regularly for summits with specific themes. One was identified as Middle East security, with the goal of normalising relations between Israel and Saudi Arabia.

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The unclassified security strategy set out how “the days of the United States propping up the entire world order like Atlas are over”.

The classified version is said to explain that the goal of global hegemony was “the wrong thing to want and it wasn’t achievable”.

It is believed to say: “After the end of the Cold War, American foreign policy elites convinced themselves that permanent American domination of the entire world was in the best interests of our country. Yet the affairs of other countries are our concern only if their activities directly threaten our interests.”

This is the logic behind the focus on policing America’s “hemisphere”, giving it the right to pressure Venezuela as it has done in recent months by destroying alleged drug-running boats and building up a huge military presence in the region.

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“We will reward and encourage the region’s governments, political parties, and movements broadly aligned with our principles and strategy,” according to the Defense One report of the document. “But we must not overlook governments with different outlooks with whom we nonetheless share interests and who want to work with us.”