European leaders have called for stronger action to defend their continent and support Ukraine, in a show of unity after Donald Trump won re-election to the White House for a second term that is likely to prove a major challenge for the bloc.

Meeting in Budapest for two days of talks hosted by Hungary’s prime minister, Viktor Orbán, an outspoken Trump ally, the EU’s 27 heads of state and government were joined on Thursday by 20 other leaders from the wider European Political Community including Ukraine’s president, Volodymyr Zelenskyy.

On the agenda were support for Ukraine, migration, trade and economic security. An informal summit of EU leaders alone will focus on Friday on the bloc’s declining competitiveness, laid bare in a report by the former Italian leader Mario Draghi.

Orbán said there had been “diverging opinions” during the day-long talks but also common ground on the need for Europe to respond to a “world-changing” US election result.

“There was agreement that Europe should take more responsibility for its peace and security. To be blunt, we cannot wait for the Americans to protect us,” he said. He had celebrated Trump’s victory with vodka rather than champagne, he added, because “I was in Kyrgyzstan, where they have different traditions”.

Trump’s victory brings unwanted further uncertainty to the continent at a time when it is already struggling to agree on common responses to its problems, including much-needed new funding tools, such as joint borrowing, for defence and economic innovation.

The return of the former president raises the prospect of a halt to US support for Ukraine, fuels doubts over Washington’s future commitment to the Nato alliance, and could herald economically disastrous tariffs on European exports.

It is also likely to bolster Europe’s advancing far-right parties at a time when the EU’s two biggest powers – Germany, whose coalition government collapsed on Wednesday, and France – are weakened by political crises at home.

The French president, Emmanuel Macron, said Europe must assert its independence from the US and defend its interests over those of geopolitical rivals at a “decisive moment in history”, adding that the bloc could not allow itself to be a weak “herbivore” surrounded by “carnivores”.

Europe must seize control of its history and could no longer “delegate” its security to the US, Macron said. “Do we want to read the history written by others – the wars launched by Vladimir Putin, the US election, China’s technological or trade choices – or do we want to write our own?”

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Macron likens Europe to a herbivore as he calls for it to 'take back control' – video

Orbán said that with the prospect of Trump returning to the White House, “the camp of those who want peace in Ukraine has increased significantly”. This was “a new situation, and Europe must react” by pushing for an early ceasefire, he said.

Zelenskyy responded that talk of introducing a ceasefire without first obtaining security guarantees for Ukraine was dangerous. “A ceasefire when there are no security guarantees … is preparation for the continuation of the occupation,” he said.

The Ukrainian president had earlier insisted that an approach of “peace through strength” was needed, saying that concessions to Moscow were unacceptable for Ukraine and would be suicidal for Europe.

Heading into the talks, the European Council president, Charles Michel, also acknowledged “differences” but said Europe aimed to be a “respected partner” for the US, adding that Washington “knows it is in its interest to show firmness when we engage with authoritarian regimes”.

The European Commission president, Ursula von der Leyen, said the EU must maintain unity.

“We have shown Europe can take responsibility by standing together. We showed it during the pandemic and the energy crisis,” she said, adding that she was looking forward to working with Trump again “in a good manner … to strengthen the transatlantic bond”.

On Russia’s full-scale invasion of Ukraine, von der Leyen said: “It is in all our interests that the autocrats of this world get a very clear message that is not the right of might, that the rule of law is important.”

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Nato’s new secretary general, Mark Rutte, said he aimed to work closely with Trump, noting that it was pressure from Washington during the former president’s first term that had pushed alliance members to boost defence spending.

Russia was “delivering the latest [weapons] technology into North Korea in return for North Korean help with the war against Ukraine”, a threat “not only to the European part of Nato, but also to the US”, he said, adding that he was looking forward to discussing with Trump “how we face these threats collectively”.

Others were more circumspect. Trump was “known sometimes for a degree of unpredictability, a degree of volatility, so we need dialogue”, Luxembourg’s prime minister, Luc Frieden, said. “We will seek dialogue, but won’t give up our principles.”

Finland’s prime minister, Petteri Orpo, said he was alarmed at the prospect of a trade war. “It should not be allowed to happen,” he said. “Let’s now try to influence the US and Trump’s future policy so that he understands the risks involved.”

Analysts have expressed significant doubts about the extent to which Europe’s often-divided leaders will be able to rise collectively to the challenge of an isolationist, “America first” presidency.

Eurointelligence analysts said: “Contrary to claims, Europe is not prepared for the economic impact of higher tariffs, the likely U-turn on Ukraine, and defence spending ultimatums. We expect the EU to divide on similar lines to the US itself.”

Some have suggested it could prove the “electroshock” the EU needs. Sébastien Maillard, of the Jacques Delors Institute, said Europeans “really have a knife at their throat … The US election result forces the EU to open its eyes.” But perhaps, he added, “it’s in situations like these that things can actually happen”.

Mujtaba Rahman, of the Eurasia Group, said: “There is some reason to believe that a Trump 2.0 presidency – a situation many EU capitals will perceive as existential to their and the EU’s interests – could galvanise EU politics to action.

“But should Trump’s attack on the EU become existential, fragmentation is one possible result that could easily spread.”