Kyiv and the West have rejected those calls and cast Russia's assault as nothing but an imperial-style land grab.
Russia's invasion in February 2022 triggered the biggest European conflict since World War II.
Tens of thousands have been killed, swathes of eastern and southern Ukraine destroyed and millions forced to flee their homes.
Trump has been growing increasingly frustrated at both Zelenskyy and Putin for not having struck a deal yet.
At a UN Security Council meeting Thursday a U.S. diplomat reaffirmed that Washington could pull back from peace efforts if it does not see progress soon.
Despite the sides having held their first peace talks in more than three years, there has been little sign of movement towards a possible compromise agreement.