In Malta’s ancient fortress capital of Valletta, Angela Merkel will on Friday find herself in a position she has often occupied since becoming German chancellor in 2005. Whenever Europe is confronted with a political challenge, she is the one who sets the pace and tone of the response.

The problem this time, as EU leaders gather on the Mediterranean island for their first summit of the year, is Donald Trump and how EU leaders should deal with the strident new occupant of the White House.

“When it comes to Trump, our point of departure is that we are up against a mode of government that is unusual for us. We don’t know whether each tweet constitutes a real political act or a joke,” said a senior European diplomat.

Relations with the new US president are not on the formal agenda; EU leaders intend to agree measures to stem the flow of migrants from Libya and to discuss a master plan to spur the EU in the Brexit era ahead of celebrations in Rome next month to mark the 60th anniversary of the bloc’s founding treaty.

But Mr Trump’s uncompromising actions since taking power, tearing up trade deals and cracking down on immigration from seven mainly Muslim countries, have intensified the uncertainty over his presidency. Doubts over his engagement with the EU follow his questioning of the validity of the Nato alliance.

As Ms Merkel campaigns for a fourth term in difficult autumn elections, the challenge presented by Mr Trump is compounding existing divisions in Europe over a range of knotty questions, from the EU response to populism to the need for fiscal flexibility and Russia’s increasing aggression in Ukraine.

Setting new diplomatic ground rules, the US president has questioned the notion of US support for European integration and placed Germany at the core of his criticism of the EU. He has questioned whether other countries will follow Britain’s exit from the bloc and his top trade adviser has accused Berlin of exploiting the euro’s weakness to gain advantage over the US.

Such remarks have sent shockwaves through Brussels. “The Americans have been behind [the European] project since it began. It wouldn’t have happened without the Marshall Plan,” said a second senior diplomat, referring to the US post-second world war aid programme for Europe. “Now it’s branded an enemy of the state — and disintegration is on the menu.”

But for all the fireworks since the US leader took office a fortnight ago, Ms Merkel has maintained her habitual caution about Mr Trump and his strident rhetoric, insisting that judgment should be formed only on the basis of the policies he executes.

Christoph Heusgen, Ms Merkel’s foreign policy adviser, says “strategic patience” is the right response. It is far better, say her officials, for any resistance to Mr Trump to come from inside the US, as seen in protests against his immigration curbs.

But the chancellor remains ready to invoke measured criticism against ideas she rejects, for example speaking out against travel curbs that put whole groups such as Muslims under “general suspicion”.

We are up against a mode of government that is unusual for us. We don’t know whether each tweet constitutes a real political act or a joke

Fabrice Pothier, non-resident senior fellow at the Atlantic Council in Washington, said Europe’s dependence on Ms Merkel’s leadership has reached a new level in the Trump era.

“Clearly, she is more central than ever. She is conscious herself of that, but she is not enough to carry Europe. Germany is basically the main shareholder but not the majority shareholder. She needs to hold her ground but she cannot do it on her own.”

Ms Merkel herself insists it is “grotesque and absurd” to suggest she should assume the mantle of leader of the free world after Mr Trump’s shock victory. But her dominance has been underscored by turmoil within Europe itself.

François Hollande, French president, is a spent force after deciding not to seek a second term this spring. Rightwing populists expect big strides in looming Dutch and German elections as well as in France. In Poland and Hungary, populists are already in power. Matteo Renzi, former Italian leader, lost office after a humiliating referendum defeat at the hands of populist campaigners.

As Brexit talks loom, Theresa May, the UK prime minister, cannot speak for other European leaders. Indeed, diplomats in Brussels have criticised her for rushing to align with Mr Trump. Mrs May will attend morning talks in Malta on immigration, but she will leave before her counterparts discuss how they might overcome the “dramatic challenges both from within and outside” that have taken the EU to a turning point.

Yet there is no consensus on the right response to Mr Trump. Some member states were displeased when Donald Tusk, president of the European Council, ranked “worrying declarations” from the US president alongside threats from China and Russia.

“Not all member states would subscribe to the idea of being rough and tough with Mr Trump,” said another EU diplomat. “France has requested co-ordination to ensure a unified European expression.”

But it remains unclear whether Europe’s leaders will be able to present a coherent message on the US president. “Everything has become more difficult with the election of Trump,” said Cem Özdemir, co-leader of the German Greens.

Ultimately for Ms Merkel, the best response lies in reinforcing the EU itself. “The citizens of Europe,” she said in a speech, “sho