Moscow, Russia - Russia said Thursday that a face-to-face meeting between Donald Trump and Vladimir Putin needed to be organized "promptly", after the two presidents held a lengthy phone call the day before.

Trump said the pair agreed to "immediately" start negotiations on the Ukraine war during the call, which marked the first direct presidential contact between Washington and Moscow in three years.

"There is definitely a need to organize such a meeting quite promptly, the heads of state have a lot to talk about," said Kremlin spokesperson Dmitry Peskov, who also confirmed that a delegation was already in the process of being formed.

Trump said Wednesday he expected to meet Putin in Saudi Arabia.

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Russia also wants to discuss European security in any negotiations with the US, Peskov said, in an apparent reference to Putin's concerns about NATO expansion.

Before launching the Ukraine invasion in 2022, Moscow demanded that the military alliance roll back to its 1997 borders – which would exclude all the Baltic states as well as Poland.

"Certainly, all issues related to security on the European continent, especially in those aspects that concern our country, the Russian Federation, should be discussed comprehensively, and we expect that to be the case," Peskov said.

Still reeling from the shock of Trump's announcement, European leaders on Thursday insisted there could be no negotiations without the direct involvement of Ukraine and its allies on the continent.