Trump, who for weeks had been threatening new sanctions against Russia for failing to halt the war, announced instead on Friday that he would meet Putin on August 15 in Alaska.
A White House official has said Trump is open to Zelenskiy attending but preparations are underway for only a bilateral meeting.
The Kremlin leader last week ruled out meeting Zelenskiy, saying conditions for such an encounter were "unfortunately still far" from being met.
Trump said a potential deal would involve "some swapping of territories to the betterment of both (sides)", compounding Ukrainian fears that it may face pressure to surrender land.
Zelenskiy says any decisions taken without Ukraine will be "stillborn" and unworkable. On Saturday the leaders of Britain, France, Germany, Italy, Poland, Finland and the European Commission said any diplomatic solution must protect the security interests of Ukraine and Europe.
"The US has the power to force Russia to negotiate seriously," EU foreign policy chief Kaja Kallas said on Sunday.Â
"Any deal between the US and Russia must have Ukraine and the EU included, for it is a matter of Ukraine's and the whole of Europe's security."
EU foreign ministers will meet on Monday to discuss next steps, she said.
NATO Secretary General Mark Rutte told US network ABC News that Friday's summit "will be about testing Putin, how serious he is on bringing this terrible war to an end".
He added: "It will be, of course, about security guarantees, but also about the absolute need to acknowledge that Ukraine decides on its own future, that Ukraine has to be a sovereign nation, deciding on its own geopolitical future."
Russia holds nearly a fifth of the country.
Rutte said a deal could not include legal recognition of Russian control over Ukrainian land, although it might include de facto recognition. He compared it to the situation after World War Two when Washington accepted that the Baltic states of Latvia, Lithuania and Estonia were de facto controlled by the Soviet Union but did not legally recognise their annexation.
Zelenskiy said on Sunday: "The end of the war must be fair, and I am grateful to everyone who stands with Ukraine and our people today."
A European official said Europe had come up with a counter-proposal to Trump's, but declined to provide details. Russian officials accused Europe of trying to thwart Trump's efforts to end the war.
"The Euro-imbeciles are trying to prevent American efforts to help resolve the Ukrainian conflict," former Russian president Dmitry Medvedev posted on social media on Sunday.
Russian Foreign Ministry spokeswoman Maria Zakharova said in a vituperative statement that the relationship between Ukraine and the European Union resembled "necrophilia".
Ukraine and its European allies have been haunted for months by the fear that Trump, keen to claim credit for making peace and hoping to seal lucrative joint business deals between the US and Russia, could align with Putin to cut a deal that would be deeply disadvantageous to Kyiv.
They had drawn some encouragement lately as Trump, having piled heavy pressure on Zelenskiy and berated him publicly in the Oval Office in February, began criticising Putin as Russia pounded Kyiv and other cities with its heaviest air attacks of the war.
But the impending Putin-Trump summit has revived fears that Kyiv and Europe could be sidelined.
US Vice President JD Vance said a negotiated settlement was unlikely to satisfy either side. "Both the Russians and the Ukrainians, probably, at the end of the day, are going to be unhappy with it," he said on Fox News' Sunday Morning Futures with Maria Bartiromo.
