"Our Donald", or "the other Donald"? European Union leaders meeting in Malta found themselves taking sides, between their summit chairman, "our Donald" Tusk, and the new U.S. president, Donald Trump.

But despite declarations of unity, EU states are split on how to respond to policies from a man who has reversed staunch postwar U.S. support for European integration and suggested others follow Britain out of a bloc he has called "a vehicle for Germany".

Tusk, a former Polish prime minister, said EU leaders gave him the "our Donald" nickname in Malta. He presented it as a sign of their support, saying before the summit that Trump posed a "threat" to the bloc, alongside Russia, China and violent Islam.

"The mood in the room was 'our Donald' and 'the other Donald'," said one person present at the talks, where Tusk also felt confident enough in his support to confirm he wants a second term as president of the European Council.

His political enemies in the Warsaw government publicly disavowed any sense of unanimity behind Tusk, however, calling his criticism of Trump a "gross abuse" and accusing him of "sowing fear" and "seeking confrontation".

Others, less publicly, said there was wider disquiet that the EU could turn its back on its Transatlantic relationship.

Such internal arguments pit historic unease, especially in France, over U.S. influence against fears of weakening a Western front against Russia and, increasingly, China. How they play out will help shape Trump's hopes, for example, of saving U.S. money spent on NATO and shifting world trade in Americans' favour.

They will also flavour the EU's Brexit talks with London - where Prime Minister Theresa May sees Britain being a bridge between Washington and Brussels - as well as efforts by some states to tighten cooperation on euro zone economic policies and other areas, notably an independent EU military capability.

"STRATEGIC AUTONOMY"

As a Pole well aware it is U.S. forces that underpin NATO's security guarantees in eastern Europe, Tusk nuanced his call to Europeans to pull together to defend their independent interests against the "superpowers, the United States, Russia and China" with an appeal to Americans to preserve "the Transatlantic bond without which global order and peace cannot survive".

But some leaders worry Trump's coolness toward NATO and the exit of well-armed Britain will fuel ambitions for Europeans to loosen that bond - notably in Paris, which has often chafed at "Anglo-American" influence and where officials say Trump shows France has been right to seek "strategic autonomy" for the EU.

"The French ... are as usual saying 'It's just the European Union now; there's no such thing as the West'," said a senior eastern European diplomat, criticising Paris's view.

"The Germans are much more cautious. There is a clear issue to be decided on whether we should seek a common ground to engage with the United States, or turn our backs."

As EU leaders prepare to map out a post-Brexit strategy at a 60th anniversary summit in Rome next month, French President Francois Hollande criticised Trump and eastern European governments he accused of raking in EU subsidies but then breaking ranks and undermining the bloc by seeking special favour from Washington.

Many in the east are especially alarmed by Trump's warmer tone toward Russia but some back his entry ban on Muslims, which echoes their own criticisms of EU refugee policies.

German Chancellor Angela Merkel took a less confrontational tone but stressed the need for "multilateralism" - a prod to Trump not to try and circumvent the EU by talking only to national leaders, and to Europeans to speak with a single voice.

Whether "the other Donald" gets that message is another matter, given a seemingly hazy grasp on who is who in Brussels. The tycoon-turned-president told an interviewer last month he had spoken to "the head of the European Union" and named his interlocutor as Jean-Claude Juncker, the EU chief executive.

In fact, however, he had spoken to "our Donald", Tusk.

"Sometimes I have an impression that the new administration does not know the EU in detail," Juncker said drily on Friday.

"But, in Europe, details matter."