The Europeans are desperate to exert some influence over a Friday meeting they have been sidelined from.
It remains unclear whether even Ukraine will take part.
Trump has said he wants to see whether Putin is serious about ending the war, now in its fourth year.
But Trump has disappointed US allies in Europe by saying Ukraine will have to give up some Russian-held territory.
He also said Russia must accept land swaps, although it remains unclear what Putin might be expected to surrender.
The Europeans and Ukraine are wary that Putin, who has waged the biggest land war in Europe since 1945 and used Russia's energy might to try to cow the EU, might secure favourable concessions and set the outlines of a peace deal without them.
In a statement early on Tuesday, the leaders said they "welcome the efforts of President Trump towards ending Russia's war of aggression against Ukraine".
But, they underlined, "the path to peace in Ukraine cannot be decided without Ukraine".
"A just and lasting peace that brings stability and security must respect international law, including the principles of independence, sovereignty, territorial integrity and that international borders must not be changed by force," they said.
Ukrainian President Volodymyr Zelenskiy has rejected the idea that Ukraine must commit to give up land to secure a ceasefire.
Russia holds shaky control over four of the country's regions, two in the country's east and two in the south.
Meanwhile, Russia appeared to be on the verge of taking an important city in the Donetsk region, as its forces were reported to be rapidly infiltrating positions north of Pokrovsk.
Military analysts using open-source information to monitor the battles say the next 24-48 hours could be critical.
Losing Pokrovsk would hand Russia an important battlefield victory before the summit.
It would also complicate Ukrainian supply lines to the Donetsk region, where the Kremlin has focused the bulk of its military efforts.
European countries fear Putin will set his sights on one of them next if he wins in Ukraine.
On Monday, Trump repeated that "there'll be some land swapping going on", and this would involve "some bad stuff for both" Ukraine and Russia.
His public rehabilitation of Putin - a pariah in most of Europe - has unnerved Ukraine's backers.
Trump was also critical of Zelenskiy, noting that Ukraine's leader had been in power for the duration of the war and said "nothing happened" during that time.
He contrasted that with Putin, who has wielded power unchallenged in Russia for decades.
It's unclear whether the Europeans were unsettled by Trump's assertion that he would travelling to Russia on Friday to meet Putin.
The summit is taking place in the US state of Alaska, which was colonised by Russia in the 18th century until Czar Alexander II sold it to the US in a land deal in 1867.
The Europeans will make a fresh attempt to rally Trump to Ukraine's cause on Wednesday at virtual meetings convened by German Chancellor Friedrich Merz.
Trump did not confirm whether he would take part, but he did say: "I'm going to get everybody's ideas" before meeting with Putin.
Hungarian Prime Minister Viktor Orban, who is Putin's closest ally in Europe and has tried to block EU support for Ukraine, was the only one of the 27 European leaders who refused to endorse Tuesday's statement.
