“I think the fact we are even together today is a really good sign,” he said. “If we have a win, long before January 20th, before I would take the presidency, long before that, I think we could work out something that is good for both sides.”

He repeated that claim several times over the past year, and most people expect him to try to start talks with Ukraine and Russia in the coming weeks. Sources in Kyiv told The Telegraph they thought Trump might appoint an envoy to broker between Ukraine and Russia before the end of this month.

But Trump has been vague on how he would achieve that deal. JD Vance, his running mate, has suggested that Ukraine should both give up occupied territory and its ambitions to join Nato in exchange for establishing a ceasefire.

That will be difficult for Ukraine to accept, and it is not obvious whether Russia would be interested in settling for the current lines when it seems to be taking more and more land. The worst fear in Kyiv is that Vladimir Putin demands more land than he currently holds, that Ukraine then refuses, and Trump cuts all aid in response, allowing Russia to press ahead with its current offensive.

‘Something out of the box’

But there is some cautious optimism in Kyiv on Wednesday morning. “A lot of people are concerned because they don’t know what to expect, but there are also a lot of people who are hoping this will actually be better, because it is something out of the box,” said Andriy Zagorodnyuk, a former defence minister. “Very few people wanted to see a continuation of the previous policy.”

Ukraine and its European allies are unlikely to resist Trump’s pressure for talks because of the implicit threat he would cut off military aid in order to force the issue. Instead, said Volodymyr Fesenko, a Kyiv-based political analyst, they will seek to make sure the talks, and whatever settlement comes out of them, are as much in Ukraine’s favour as possible.

For example, Kyiv may accept the path to Nato is blocked but ask for separate American security guarantees, akin to its deals with Israel and South Korea.

And they hope that if Putin refuses peace on Trump’s terms, the Republican will radically jack up sanctions on Russian oil and increase aid to Ukraine in response.

Europe

The first leader to congratulate Trump was Viktor Orban, the prime minister of Hungary, who describes the former president as a “good friend”.

Mr Orban, who has refused to send weapons to Ukraine, suggested before the election that should Trump win, Europe would have to adjust its stance on the war. “If Americans switch to peace, then we also need to adapt,” the Hungarian prime minister said.